Ewald–Oseen extinction theorem

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oscillation (EM fields of oscillating charges). Due to the linearity of Maxwell equations, one expects the total field at any point in space to be the sum of the original field and the field produced by oscillating electrons. This result is, however, counterintuitive to the practical wave one observes in the dielectric moving at a speed of c/n, where n is the medium index of refraction. The Ewald–Oseen extinction theorem seek to address the disconnect by demonstrating how the superposition of these two waves reproduces the familiar result of a wave that moves at a speed of c/n.

10204: 2132: 1312: 6485: 6977: 1677: 10698:{\displaystyle \mathbf {E} (z,t)=\left\{{\begin{array}{l}{\mathbf {E} _{0}e^{i\left(k_{0}z-\omega t\right)}-{\frac {\mathbf {P} }{2\epsilon _{0}}}{\frac {k_{0}}{k+k_{0}}}e^{-i\left(k_{0}z+\omega t\right)}}&{z<0}\\{\mathbf {E} _{0}e^{i\left(k_{0}z-\omega t\right)}-{\frac {\mathbf {P} }{2\epsilon _{0}}}{\frac {k_{0}}{k-k_{0}}}e^{i\left(k_{0}z-\omega t\right)}-{\frac {\mathbf {P} }{\epsilon _{0}}}{\frac {k_{0}^{2}}{k_{0}^{2}-k^{2}}}e^{i(kz-\omega t)}}&{z>0.}\end{array}}\right.} 2446: 1877: 913: 8025: 9688: 141: 11630: 1041: 10050: 1424: 6657: 2143: 714: 6162: 9313: 9496: 7482: 6067: 11315: 2127:{\displaystyle {\begin{aligned}\nabla \times \nabla \times \mathbf {E} _{\mathrm {rad} }&=-{\frac {\partial }{\partial t}}(\nabla \times \mathbf {B} _{\mathrm {rad} })\\\nabla \times \nabla \times \mathbf {E} _{\mathrm {rad} }&=-{\frac {\partial }{\partial t}}\left(\mu _{0}\mathbf {J} +\epsilon _{0}\mu _{0}{\frac {\partial \mathbf {E} _{\mathrm {rad} }}{\partial t}}\right)\end{aligned}}} 2911: 9821: 1307:{\displaystyle {\begin{array}{l}{\nabla \cdot \mathbf {E} _{\mathrm {rad} }=0}\\{\nabla \cdot \mathbf {B} _{\mathrm {rad} }=0}\\{\nabla \times \mathbf {E} _{\mathrm {rad} }=-\partial \mathbf {B} _{\mathrm {rad} }/\partial t}\\{\nabla \times \mathbf {B} _{\mathrm {rad} }=\mu _{0}\mathbf {J} +\epsilon _{0}\mu _{0}\partial \mathbf {E} _{\mathrm {rad} }/\partial t}\end{array}}} 9491: 5024: 8989: 8566: 8807: 1672:{\displaystyle {\begin{array}{l}{\nabla \cdot \mathbf {E} _{\mathrm {vac} }=0}\\{\nabla \cdot \mathbf {B} _{\mathrm {vac} }=0}\\{\nabla \times \mathbf {E} _{\mathrm {vac} }=-\partial \mathbf {B} _{\mathrm {vac} }/\partial t}\\{\nabla \times \mathbf {B} _{\mathrm {vac} }=\epsilon _{0}\mu _{0}\partial \mathbf {E} _{\mathrm {vac} }/\partial t}\end{array}}} 6972:{\displaystyle I:=\int _{-\infty }^{\infty }dx^{\prime }\int _{-\infty }^{\infty }dy^{\prime }{\frac {e^{ik_{0}\left|\mathbf {r} -\mathbf {r} ^{\prime }\right|}}{\left|\mathbf {r} -\mathbf {r} ^{\prime }\right|}}=\int _{0}^{2\pi }d\varphi '\int _{0}^{\infty }d\rho '{\frac {e^{ik_{0}R}}{R}}=2\pi \int _{0}^{\infty }d\rho '{\frac {e^{ik_{0}R}}{R}}.} 3135: 2441:{\displaystyle {\begin{aligned}(\nabla \times \nabla \times \mathbf {E} )_{i}&=\epsilon _{ijk}\epsilon _{klm}\partial _{j}\partial _{l}E_{m}\\&=(\delta _{il}\delta _{j\mathrm {m} }-\delta _{i\mathrm {m} }\delta _{jl})\partial _{j}\partial _{l}E_{m}\\&=\partial _{i}(\partial _{j}E_{j})-\partial _{j}\partial _{j}E_{i}\end{aligned}}} 908:{\displaystyle {\begin{aligned}\nabla \cdot \mathbf {E} &=0\\\nabla \cdot \mathbf {B} &=0\\\nabla \times \mathbf {E} &=-{\frac {\partial \mathbf {B} }{\partial t}}\\\nabla \times \mathbf {B} &={\boldsymbol {\mu }}_{0}\mathbf {J} +\epsilon _{0}{\boldsymbol {\mu }}_{0}{\frac {\partial \mathbf {E} }{\partial t}}\end{aligned}}} 2715: 11654:.) Unfortunately, the extinction length of light in space nullifies the results of any such experiments using visible light, especially when taking account of the thick cloud of stationary gas surrounding such stars. However, experiments using X-rays emitted by binary pulsars, with much longer extinction length, have been successful. 6480:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e,p} }(\mathbf {r} ,t)={\frac {\mathbf {P} _{0}e^{i(kz-\omega t)}}{4\pi \epsilon _{0}}}\int _{0}^{\infty }dz'e^{ik\left(z'-z\right)}\int _{-\infty }^{\infty }dx'\int _{-\infty }^{\infty }dy'{\frac {e^{ik_{0}\left|\mathbf {r} -\mathbf {r} '\right|}}{\left|\mathbf {r} -\mathbf {r} '\right|}}.} 4898: 9683:{\displaystyle {\begin{aligned}\mathbf {E} _{\mathrm {p} }&=\nabla \times \nabla \times {\boldsymbol {\pi }}_{\mathrm {e} }-{\frac {\mathbf {P} }{\epsilon _{0}}}\\&=\nabla (\nabla \cdot {\boldsymbol {\pi }}_{\mathrm {e,p} })-\nabla ^{2}{\boldsymbol {\pi }}_{\mathrm {e,p} }-{\frac {\mathbf {P} }{\epsilon _{0}}}.\end{aligned}}} 5862: 3349: 8020:{\displaystyle {\begin{aligned}I&=2\pi \int _{\left|z'-z\right|}^{\infty }dRe^{ik_{0}R}\\&=2\pi \lim _{\epsilon \to 0}\int _{\left|z'-z\right|}^{\infty }dRe^{(ik_{0}-\epsilon )R}\\&=\left.2\pi \lim _{\epsilon \to 0}\left\right|_{\left|z'-z\right|}^{\infty }\\&=2\pi \lim _{\epsilon \to 0}\left.\end{aligned}}} 11625:{\displaystyle \mathbf {E} (z,t)=\left\{{\begin{array}{l}{\mathbf {E} _{0}e^{i\left(k_{0}z-\omega t\right)}-\left({\frac {n-1}{n+1}}\right)\mathbf {E} _{0}e^{-i\left(k_{0}z+\omega t\right)}}&{z<0}\\{\left({\frac {2}{n+1}}\right)\mathbf {E} _{0}e^{i\left(nk_{0}z-\omega t\right)}}&{z>0.}\end{array}}\right.} 9361: 4905: 1036: 5324: 10045:{\displaystyle {\begin{aligned}\mathbf {E} _{\mathrm {p} }&=-{\frac {1}{c^{2}}}{\frac {\partial ^{2}{\boldsymbol {\pi }}_{\mathrm {e,p} }}{\partial t^{2}}}\\&=-{\frac {1}{c^{2}}}(-i\omega )^{2}{\boldsymbol {\pi }}_{\mathrm {e,p} }\\&=k_{0}^{2}{\boldsymbol {\pi }}_{\mathrm {e,p} }\end{aligned}}} 11649:

predicts that the speed of light in vacuum is independent of the velocity of the source emitting it. This widely believed prediction has been occasionally tested using astronomical observations. For example, in a binary star system, the two stars are moving in opposite directions, and one might test

11642:

The characteristic "extinction length" of a medium is the distance after which the original wave can be said to have been completely replaced. For visible light, traveling in air at sea level, this distance is approximately 1 mm. In interstellar space, the extinction length for light is 2 light

127:

When an electromagnetic wave enters a dielectric medium, it excites (resonates) the material's electrons whether they are free or bound, setting them into a vibratory state with the same frequency as the wave. These electrons will in turn radiate their own electromagnetic fields as a result of their

96:

The Ewald–Oseen extinction theorem says that the light emitted by the atoms has a component traveling at the speed of light in vacuum, which exactly cancels out ("extinguishes") the original light wave. Additionally, the light emitted by the atoms has a component which looks like a wave traveling at

11643:

years. At very high frequencies, the electrons in the medium can't "follow" the original wave into oscillation, which lets that wave travel much further: for 0.5 MeV gamma rays, the length is 19 cm of air and 0.3 mm of Lucite, and for 4.4 GeV, 1.7 m in air, and 1.4 mm in carbon.

8247: 2959: 36:, who proved the theorem in crystalline and isotropic media, respectively, in 1916 and 1915. Originally, the theorem applied to scattering by an isotropic dielectric objects in free space. The scope of the theorem was greatly extended to encompass a wide variety of bianisotropic media. 7139: 8573: 4769: 9308:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e,p} }(z,t)=-{\frac {\mathbf {P} e^{-i\omega t}}{2\epsilon _{0}k_{0}}}{\begin{cases}{{\frac {1}{k+k_{0}}}e^{-ik_{0}z}}&{z<0}\\{{\frac {2k_{0}}{k_{0}^{2}-k^{2}}}e^{ikz}+{\frac {1}{k-k_{0}}}e^{ik_{0}z}}&{z>0.}\end{cases}}} 11130: 10199: 2562: 5131: 8242: 3219: 3847: 5434: 3478: 710:

assume that the wavelength is much larger than the average separation of atoms so that the medium can be considered continuous. We use the usual macroscopic E and B fields and take the medium to be nonmagnetic and neutral so that Maxwell's equations read

136:

The following is a derivation based on a work by Ballenegger and Weber. Let's consider a simplified situation in which a monochromatic electromagnetic wave is normally incident on a medium filling half the space in the region z>0 as shown in Figure 1.

2906:{\displaystyle \nabla ^{2}\mathbf {E} _{\mathrm {rad} }={\frac {\partial }{\partial t}}(\mu _{0}{\sigma }\mathbf {E} _{\mathrm {vac} }+\mu _{0}{\sigma }\mathbf {E} _{\mathrm {rad} }+\epsilon _{0}\mu _{0}\partial \mathbf {E} _{\mathrm {rad} }/\partial t)} 1417: 918: 5200: 708: 553: 6062:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e,p} }(\mathbf {r} ,t)={\frac {1}{4\pi \epsilon _{0}}}\int d^{3}r'{\frac {\mathbf {P} \left(\mathbf {r} ',t-\left|\mathbf {r} -\mathbf {r} '\right|/c\right)}{\left|\mathbf {r} -\mathbf {r} '\right|}}.} 357: 7320: 10997: 5653: 557:

This to say that the radiated field cancels out the incident field and creates a transmitted field traveling within the medium at speed c/n. Using the same logic, outside the medium the radiated field produces the effect of a reflected field

2661: 7412: 3702: 11216: 3958: 4070: 1796: 10835: 9486:{\displaystyle \nabla \times (\nabla \times \mathbf {{\boldsymbol {\pi }}_{\mathrm {e,p} }} )=\nabla (\nabla \cdot \mathbf {{\boldsymbol {\pi }}_{\mathrm {e,p} }} )-\nabla ^{2}\mathbf {{\boldsymbol {\pi }}_{\mathrm {e,p} }} ,} 3212: 5019:{\displaystyle \mathbf {E} =\nabla \times \nabla \times {\boldsymbol {\pi }}_{\mathrm {e} }-{\frac {\mathbf {P} }{\epsilon _{0}}}-{\frac {\partial }{\partial t}}\left(\nabla \times {\boldsymbol {\pi }}_{\mathrm {m} }\right),} 6157: 148:

The electric field at a point in space is the sum of the electric fields due to all the various sources. In our case, we separate the fields in two categories based on their generating sources. We denote the incident field

11002: 10057: 6984: 2453: 5060: 4325: 4574: 5764: 9739: 11308: 5331: 8561:{\displaystyle {\begin{aligned}I&=2\pi \lim _{\epsilon \to 0}\left\\&=-2\pi {\frac {e^{ik_{0}{\left|z'-z\right|}}}{ik_{0}}}\\&=2\pi i{\frac {e^{ik_{0}{\left|z'-z\right|}}}{k_{0}}}.\end{aligned}}} 7210: 4186: 6653: 3130:{\displaystyle \nabla ^{2}\mathbf {E} _{\mathrm {rad} }+\mu _{0}\omega ^{2}\left(\epsilon _{0}+i\sigma /\omega \right)\mathbf {E} _{\mathrm {rad} }=-i\mu _{0}\omega \sigma \mathbf {E} _{\mathrm {vac} }(z)} 8110: 3735: 2710: 1882: 10878: 5812: 4645:

The following is a derivation based on a work by Wangsness and a similar derivation found in chapter 20 of Zangwill's text, Modern Electrodynamics. The setup is as follows, let the infinite half-space

3379: 5707: 8115: 4380: 3544: 8802:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e,p} }(z,t)={\frac {i\mathbf {P} _{0}e^{i(kz-\omega t)}}{2k_{0}\epsilon _{0}}}\int _{0}^{\infty }dz'e^{ik\left(z'-z\right)}e^{ik_{0}\left|z-z'\right|}} 9352: 8846: 6602: 5853: 1339: 4893:{\displaystyle \nabla ^{2}{\boldsymbol {\pi }}_{\mathrm {e} }-{\frac {1}{c^{2}}}{\frac {\partial ^{2}{\boldsymbol {\pi }}_{\mathrm {e} }}{\partial t^{2}}}=-{\frac {\mathbf {P} }{\epsilon _{0}}}.} 11142: 9826: 9501: 8252: 7487: 5195: 5164: 5055: 4764: 2148: 719: 590: 435: 239: 11634:

This is exactly the result as expected. There is only one wave inside the medium and it has wave speed reduced by n. The expected reflection and transmission coefficients are also recovered.

5486: 4222: 246: 1872: 396: 184: 10886: 427: 5552: 8055: 7475: 3216:

For the complete solution, we add to the particular solution the general solution of the homogeneous equation which is a superposition of plane waves traveling in arbitrary directions

4445: 3344:{\displaystyle \left(\mathbf {E} _{\mathrm {rad} }^{c}\right)_{i}=\int g_{i}({\boldsymbol {\theta }},{\boldsymbol {\phi }})\exp \left(i\mathbf {k} '\cdot \mathbf {r} \right)d\Omega } 8932: 9816: 1336:

includes the true and polarization current induced in the material by the outside electric field. We assume a linear relationship between the current and the electric field, hence

7215: 12032: 11137: 10742: 7325: 4635: 4606: 4263: 2954: 585: 7447: 5527: 3620: 9785: 1832: 11240: 9761: 8888: 4136: 4114: 3566: 2586: 1687: 1334: 10747: 3874: 3482:

Note that we have taken the solution as a coherent superposition of plane waves. Because of symmetry, we expect the fields to be the same in a plane perpendicular to the

3140: 4497: 3995: 2591: 1031:{\displaystyle \mathbf {E} =\mathbf {E} _{\mathrm {vac} }+\mathbf {E} _{\mathrm {rad} },\quad \mathbf {B} =\mathbf {B} _{\mathrm {vac} }+\mathbf {B} _{\mathrm {rad} }} 6537: 6512: 3374: 8984: 8958: 5319:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e} }(\mathbf {r} ,t)={\boldsymbol {\pi }}_{e,h}(\mathbf {r} ,t)+{\boldsymbol {\pi }}_{\mathrm {e,p} }(\mathbf {r} ,t).} 4723: 4696: 4670: 4471: 3730: 3615: 3991: 8866: 5547: 4402: 4092: 3869: 3586: 3500: 4268: 63:. Although this fact is famous and familiar, it is actually quite strange and surprising when you think about it microscopically. After all, according to the 4502: 4094:

to a familiar form of the index of refraction of a linear isotropic dielectric. To do so, we remember that in a linear dielectric an applied electric field

104:

A more complete description can be found in Classical Optics and its Applications, by Masud Mansuripur. A proof of the classical theorem can be found in

11245: 6159:

More detail about this assumption is discussed by Wangsness. Plugging this into the integral and expressing in terms of Cartesian coordinates produces

6074: 7144: 52:

works and where it comes from, starting from microscopic physics. The Ewald–Oseen extinction theorem is one part of that derivation (as is the

5057:

is 0 since the material is assumed to be non-magnetizable and there is no external magnetic field. Therefore the electric field simplifies to

4330: 28:, is a theorem that underlies the common understanding of scattering (as well as refraction, reflection, and diffraction). It is named after 5715: 9695: 4728: 189: 11125:{\displaystyle e^{i\left(k_{0}z-\omega t\right)}\Rightarrow 0=\mathbf {E} _{0}-{\frac {\chi }{2}}{\frac {k_{0}}{k-k_{0}}}\mathbf {E} .} 10194:{\displaystyle \mathbf {E} (z,t)=\mathbf {E} _{0}e^{i\left(k_{0}z-\omega t\right)}+k_{0}^{2}{\boldsymbol {\pi }}_{\mathrm {e,p} }(z,t)} 7134:{\displaystyle R^{2}=\rho ^{2}+\left|z'-z\right|^{2}\Rightarrow \rho ^{2}=R^{2}-\left|z'-z\right|^{2}\Rightarrow \rho \,d\rho =R\,dR} 4141: 3871:

is the sum of the incident and radiated fields at that position. Adding the two components inside the medium, we get the total field

2557:{\displaystyle \nabla \times \nabla \times \mathbf {E} _{rad}=\nabla (\nabla \cdot \mathbf {E} _{rad})-\nabla ^{2}\mathbf {E} _{rad}} 44:

An important part of optical physics theory is starting with microscopic physics—the behavior of atoms and electrons—and using it to

8060: 5126:{\displaystyle \mathbf {E} =\nabla \times \nabla \times {\boldsymbol {\pi }}_{\mathrm {e} }-{\frac {\mathbf {P} }{\epsilon _{0}}}.} 152: 8237:{\displaystyle \lim _{\epsilon \to 0}e^{(ik_{0}-\epsilon )\infty }=\lim _{\epsilon \to 0}e^{ik_{0}\infty }e^{-\epsilon \infty }=0} 6071:

Since the initial electric field is polarizing the material, the polarization vector must have the same space and time dependence

2666: 398:

has this form. However, we already know that inside the medium, z>0, we will only observe what we call the transmitted E-field

10840: 5769: 5660: 12027: 6607: 11731: 4407: 9320: 8814: 6545: 5821: 5429:{\displaystyle \mathbf {E} (\mathbf {r} ,t)=\mathbf {E} _{h}(\mathbf {r} ,t)+\mathbf {E} _{\mathrm {p} }(\mathbf {r} ,t).} 5169: 5138: 5029: 4738: 11716:

The Ewald-Oseen Extinction Theorem and the Extended Boundary Condition Method, in: The World of Applied Electromagnetics

9355: 3505: 2137: 5445: 4191: 3842:{\displaystyle \mathbf {E} _{\mathrm {rad} }=-\mathbf {E} _{\mathrm {vac} }(z)+\mathbf {E} _{T}\exp \left(ik'z\right)} 11883: 11777: 11696: 5439: 3473:{\displaystyle k^{\prime 2}=\mu _{0}\epsilon _{0}\omega ^{2}\left(1+i{\frac {\sigma }{\epsilon _{0}\omega }}\right)} 11651: 11312:

Both of these results can be substituted into the expression for the electric field to obtain the final expression

1840: 1681:

The two sets of Maxwell equations are coupled since the vacuum electric field appears in the current density term.

364: 401: 59:

When light traveling in vacuum enters a transparent medium like glass, the light slows down, as described by the

144:

Figure 1: The half-space z>0 is a dielectric material with susceptibility χ. The half-space z<0 is vacuum.

8032: 7452: 1874:, we take the curl of the third equation in the first set of Maxwell equation and combine it with the fourth. 1412:{\displaystyle \mathbf {J} ={\sigma }\left(\mathbf {E} _{\mathrm {vac} }+\mathbf {E} _{\mathrm {rad} }\right)} 9818:. Also, notice that the second and third terms are equivalent to the inhomogeneous wave equation, therefore, 6540: 11714:

Lakhtakia, Akhlesh (2017), "The Ewald–Oseen Extinction Theorem and the Extended Boundary Condition Method",

703:{\displaystyle \mathbf {E} _{\mathrm {rad} }(z,t)=-\mathbf {E} _{\mathrm {vac} }(z,t)-\mathbf {E} _{R}(z,t)} 548:{\displaystyle \mathbf {E} _{\mathrm {rad} }(z,t)=-\mathbf {E} _{\mathrm {vac} }(z,t)+\mathbf {E} _{T}(z,t)} 9790: 4473:, one imposes the condition of a wave traveling to the left. By setting the conductivity in this region 9354:

directly into the expression for the electric field, several simplifications can be made. Begin with the

53: 352:{\displaystyle \mathbf {E} (z,t)=\mathbf {E} _{\mathrm {vac} }(z,t)+\mathbf {E} _{\mathrm {rad} }(z,t).} 11831:

Wangsness, Roald K. (1981-10-01). "Effect of matter on the phase velocity of an electromagnetic wave".

10710: 8896: 4611: 4582: 4227: 2918: 561: 11134:

The first relation quickly yields the wave vector in the dielectric in terms of the incident wave as

10992:{\displaystyle e^{i\left(kz-\omega t\right)}\Rightarrow 1=-\chi {\frac {k_{0}^{2}}{k_{0}^{2}-k^{2}}}} 7419: 5491: 243:

The total field at any point z in space is then given by the superposition of the two contributions,

9766: 9094: 4188:. When the electric field changes, the induced charges move and produces a current density given by 11242:

in the second expression yields the polarization vector in terms of the incident electric field as

5648:{\displaystyle \mathbf {E} _{h}(\mathbf {r} ,t)=\mathbf {E} _{0}e^{i\left(k_{0}z-\omega t\right)}.} 2956:, the time derivatives are straightforward and we obtain the following inhomogeneous wave equation 1801: 89:

at the (slower) speed of light in glass. Yet when the waves are added up, they surprisingly create

11223: 9744: 8871: 4119: 4097: 3549: 2569: 1317: 5135:

In order to calculate the electric field we must first solve the inhomogeneous wave equation for

4699: 2656:{\displaystyle {\sigma }\left(\mathbf {E} _{\mathrm {vac} }+\mathbf {E} _{\mathrm {rad} }\right)} 64: 4476: 11747: 11688: 8986:. Again, a convergence factor must be introduced to evaluate both integrals and the result is 78:(Light is an oscillating electromagnetic field that pushes electrons back and forth, emitting 3617:, we expect a wave traveling to the right. The solution to the homogeneous equation becomes, 8963: 8937: 7315:{\displaystyle \rho =0={\sqrt {R^{2}-\left|z'-z\right|^{2}}}\Rightarrow R=\left|z'-z\right|} 4705: 4675: 4649: 4450: 3709: 3594: 11995: 11956: 11916: 11840: 11683: 106: 48:

the familiar, macroscopic, laws of optics. In particular, there is a derivation of how the

11211:{\displaystyle {\begin{aligned}k&={\sqrt {1+\chi }}k_{0}\\&=nk_{0}.\end{aligned}}} 3965: 8: 7407:{\displaystyle \rho =\infty ={\sqrt {R^{2}-\left|z'-z\right|^{2}}}\Rightarrow R=\infty .} 5815: 60: 11999: 11960: 11920: 11844: 6517: 6492: 3697:{\displaystyle \mathbf {E} _{\mathrm {rad} }^{c}=\mathbf {E} _{T}\exp \left(ik'z\right)} 3354: 11947:

Brecher, K. (1977). "Is the speed of light independent of the velocity of the source".

11755: 11646: 8851: 5856: 5532: 4387: 4077: 3854: 3571: 3485: 33: 101:

wave in the glass is the slow wave, consistent with what we expect from basic optics.

11879: 11856: 11813: 11773: 11727: 11692: 1791:{\displaystyle \mathbf {E} _{\mathrm {vac} }(z,t)=\mathbf {E} _{\mathrm {vac} }\exp,} 1684:

For a monochromatic wave at normal incidence, the vacuum electric field has the form

111: 10830:{\displaystyle \mathbf {E} (z>0,t)=\mathbf {E} e^{i\left(k_{0}z-\omega t\right)}} 3953:{\displaystyle \mathrm {E} (z)=\mathrm {E} _{T}\exp \left(ik'z\right),\qquad z>0} 3706:

Adding this to the particular solution, we get the radiated wave inside the medium (

12003: 11964: 11924: 11848: 11805: 11765: 11719: 3207:{\displaystyle \mathbf {E} _{\mathrm {rad} }^{P}=-\mathbf {E} _{\mathrm {vac} }(z)} 79: 49: 29: 4065:{\displaystyle n=ck'/\omega ={\sqrt {1+i{\frac {\sigma }{\epsilon _{0}\omega }}}}} 11793: 11769: 11723: 11968: 11907:(1962), "Experimental Evidence for the Second Postulate of Special Relativity", 6152:{\displaystyle \mathbf {P} (\mathbf {r} ,t)=\mathbf {P} _{0}e^{i(kz-\omega t)}.} 1421:

The set of Maxwell equations outside the dielectric has no current density term

186:

and the sum of the fields generated by the oscillating electrons in the medium

12007: 12021: 11860: 11817: 4732: 85:

Individually, each of these waves travels at the speed of light in vacuum,

11347: 10236: 4320:{\displaystyle \mathbf {J} =-i\epsilon _{0}\omega \chi _{e}\mathbf {E} ,} 1429: 1046: 140: 7477:

into the integrand since it does not change the value of the integral,

4569:{\displaystyle \mathrm {E} (z)=\mathrm {E} _{R}\exp \left(-ikz\right),} 11928: 587:

traveling at speed c in the opposite direction to the incident field.

11983: 11904: 11678: 11637: 5759:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e,p} }(\mathbf {r} ,t)} 110:, by Born and Wolf., and that of its extension has been presented by 11852: 11809: 9734:{\displaystyle \nabla \cdot {\boldsymbol {\pi }}_{\mathrm {e,p} }=0} 11760: 11674: 11650:

the prediction by analyzing their light. (See, for instance, the

10707:

Now focus on the field inside the dielectric. Using the fact that

8893:

This integration must be split into two due to the absolute value

11303:{\displaystyle \mathbf {P} =2\epsilon _{0}(n-1)\mathbf {E} _{0}.} 11687:(7th ed.), Cambridge: Cambridge University Press, p. 4731:

for the electric field can be written in terms of the electric

4181:{\displaystyle \mathbf {P} =\epsilon _{0}\chi _{e}\mathbf {E} } 17: 74:

The light waves emitted by oscillating electrons in the glass.

8105:{\displaystyle \lim _{\epsilon \to 0}e^{-\epsilon \infty }=0} 4902:

The electric field in terms of the Hertz vectors is given as

2915:

Realizing that all the fields have the same time dependence

2705:{\displaystyle \nabla \cdot \mathbf {E} _{\mathrm {rad} }=0} 11794:"The Ewald–Oseen extinction theorem and extinction lengths" 11619: 10873:{\displaystyle \mathbf {P} =\epsilon _{0}\chi \mathbf {E} } 10692: 9301: 7692: 7205:{\displaystyle \rho ={\sqrt {R^{2}-\left|z'-z\right|^{2}}}} 5807:{\displaystyle \mathbf {E} _{\mathrm {p} }(\mathbf {r} ,t)} 8570:

Now, plugging this result back into the z-integral yields

5702:{\displaystyle {\boldsymbol {\pi }}_{e,h}(\mathbf {r} ,t)} 6648:{\displaystyle \left|\mathbf {r} -\mathbf {r} '\right|=R} 4375:{\displaystyle \sigma =-i\epsilon _{0}\omega \chi _{e}.} 11986:(1964). "Velocity of Gamma Rays from a Moving Source". 5488:, is the initial plane wave traveling with wave vector 2136:

We simplify the double curl in a couple of steps using

12033:

Scattering, absorption and radiative transfer (optics)

11754:, Cambridge: Cambridge University Press, p. 209, 4384:

Then substituting the conductivity in the equation of

117: 11318: 11248: 11226: 11140: 11005: 10889: 10843: 10750: 10713: 10207: 10060: 9824: 9793: 9769: 9747: 9698: 9499: 9364: 9347:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e,p} }} 9323: 8992: 8966: 8940: 8899: 8874: 8854: 8841:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e,p} }} 8817: 8576: 8250: 8118: 8063: 8035: 7485: 7455: 7422: 7328: 7218: 7147: 6987: 6660: 6610: 6597:{\displaystyle (x,y,z)\rightarrow (\rho ,\varphi ,z)} 6548: 6520: 6495: 6165: 6077: 5865: 5848:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e,p} }} 5824: 5772: 5718: 5663: 5555: 5535: 5494: 5448: 5334: 5203: 5172: 5141: 5063: 5032: 4908: 4772: 4741: 4708: 4678: 4652: 4614: 4585: 4505: 4479: 4453: 4410: 4390: 4333: 4271: 4230: 4224:. Since the time dependence of the electric field is 4194: 4144: 4122: 4100: 4080: 3998: 3968: 3877: 3857: 3738: 3712: 3623: 3597: 3574: 3552: 3508: 3488: 3382: 3357: 3222: 3143: 2962: 2921: 2718: 2669: 2594: 2572: 2456: 2146: 1880: 1843: 1804: 1690: 1427: 1342: 1320: 1044: 921: 717: 593: 564: 438: 404: 367: 249: 192: 155: 11792:

Ballenegger, Vincent C.; Weber, T. A. (1999-07-01).

4637:, are only adopted to match what we already expect. 97:

the slower speed of light in glass. Altogether, the

11673: 5709:since we are only interested in finding the field. 5190:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e} }} 5159:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e} }} 5050:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {m} }} 4759:{\displaystyle {\boldsymbol {\pi }}_{\mathrm {e} }} 1038:the set of Maxwell equations inside the dielectric 234:{\displaystyle \mathbf {E} _{\mathrm {rad} }(z,t).} 11638:Extinction lengths and tests of special relativity 11624: 11302: 11234: 11210: 11124: 10991: 10872: 10829: 10736: 10697: 10193: 10044: 9810: 9779: 9755: 9733: 9682: 9485: 9346: 9307: 8978: 8952: 8926: 8882: 8860: 8840: 8801: 8560: 8236: 8104: 8049: 8019: 7469: 7441: 7406: 7314: 7204: 7133: 6971: 6647: 6596: 6531: 6506: 6479: 6151: 6061: 5847: 5806: 5758: 5701: 5647: 5541: 5521: 5480: 5428: 5318: 5189: 5158: 5125: 5049: 5018: 4892: 4758: 4717: 4698:be a uniform, isotropic, dielectric material with 4690: 4664: 4629: 4600: 4568: 4491: 4465: 4439: 4396: 4374: 4319: 4257: 4216: 4180: 4130: 4108: 4086: 4064: 3985: 3952: 3863: 3841: 3724: 3696: 3609: 3580: 3560: 3539:{\displaystyle \mathbf {k} '\cdot \mathbf {a} =0,} 3538: 3494: 3472: 3368: 3343: 3206: 3129: 2948: 2905: 2704: 2655: 2580: 2556: 2440: 2126: 1866: 1826: 1790: 1671: 1411: 1328: 1306: 1030: 907: 702: 579: 547: 421: 390: 351: 233: 178: 11981: 11718:, Cham, Switzerland: Springer, pp. 481–513, 3962:This wave travels inside the dielectric at speed 429:which travels through the material at speed c/n. 12019: 11791: 8272: 8174: 8120: 8065: 7839: 7702: 7588: 5481:{\displaystyle \mathbf {E} _{h}(\mathbf {r} ,t)} 4217:{\displaystyle \partial \mathbf {P} /\partial t} 67:, the light in the glass is a superposition of: 11975: 11752:Classical Optics and its Applications (2nd ed.) 11669: 11667: 10837:recall also that inside the dielectric we have 5818:method on the inhomogeneous wave equation for 4447:which is a more familiar form. For the region 8890:, which was expected for the given symmetry. 3376:is found from the homogeneous equation to be 1867:{\displaystyle \mathbf {E} _{\mathrm {rad} }} 391:{\displaystyle \mathbf {E} _{\mathrm {vac} }} 179:{\displaystyle \mathbf {E} _{\mathrm {vac} }} 11664: 5197:in the homogeneous and particular solutions 3591:Since there are no boundaries in the region 915:both the total electric and magnetic fields 11946: 11709: 11707: 4729:inhomogeneous electromagnetic wave equation 422:{\displaystyle \mathbf {E} _{\mathrm {T} }} 11745: 9787:dependence and is always perpendicular to 6489:First, consider only the integration over 11942: 11940: 11938: 11903: 11830: 11759: 11739: 11713: 8050:{\displaystyle \epsilon \in \mathbb {R} } 8043: 7470:{\displaystyle \epsilon \in \mathbb {R} } 7463: 7124: 7111: 4579:Note that the coefficients nomenclature, 93:a wave that travels at the slower speed. 11873: 11704: 11220:Using this result and the definition of 4640: 139: 11899: 11897: 11895: 10158: 10020: 9975: 9885: 9707: 9633: 9597: 9539: 9461: 9423: 9383: 9326: 8995: 8820: 8579: 6168: 5868: 5827: 5721: 5666: 5278: 5240: 5206: 5175: 5144: 5086: 5035: 4996: 4931: 4832: 4785: 4744: 4440:{\displaystyle n={\sqrt {1+\chi _{e}}}} 3291: 3283: 869: 839: 12020: 11935: 10883:Then by coefficient matching we find, 8934:inside the integrand. The regions are 4672:be vacuum and the infinite half-space 10744:is complex, we may immediately write 9811:{\displaystyle {\hat {\mathbf {z} }}} 11892: 11748:"The Ewald–Oseen extinction theorem" 7416:Then introduce a convergence factor 4327:which implies that the conductivity 24:, sometimes referred to as just the 4138:proportional to the electric field 3568:is a displacement perpendicular to 118:Derivation from Maxwell's equations 13: 10170: 10164: 10032: 10026: 9987: 9981: 9905: 9897: 9891: 9874: 9837: 9719: 9713: 9699: 9645: 9639: 9622: 9609: 9603: 9589: 9583: 9545: 9531: 9525: 9512: 9473: 9467: 9449: 9435: 9429: 9414: 9408: 9395: 9389: 9374: 9365: 9338: 9332: 9007: 9001: 8832: 8826: 8702: 8591: 8585: 8341: 8223: 8207: 8165: 8091: 7891: 7817: 7634: 7537: 7398: 7335: 6920: 6855: 6801: 6769: 6724: 6711: 6706: 6693: 6680: 6675: 6378: 6373: 6349: 6344: 6283: 6180: 6174: 5880: 5874: 5839: 5833: 5814:, is found using a time dependent 5781: 5733: 5727: 5657:We do not need to explicitly find 5400: 5328:Linearity then allows us to write 5290: 5284: 5212: 5181: 5150: 5092: 5078: 5072: 5041: 5002: 4988: 4974: 4970: 4937: 4923: 4917: 4846: 4838: 4821: 4791: 4774: 4750: 4525: 4507: 4208: 4195: 3897: 3879: 3779: 3776: 3773: 3753: 3750: 3747: 3638: 3635: 3632: 3388: 3338: 3242: 3239: 3236: 3189: 3186: 3183: 3158: 3155: 3152: 3112: 3109: 3106: 3067: 3064: 3061: 2987: 2984: 2981: 2964: 2894: 2883: 2880: 2877: 2866: 2837: 2834: 2831: 2799: 2796: 2793: 2758: 2754: 2743: 2740: 2737: 2720: 2690: 2687: 2684: 2670: 2642: 2639: 2636: 2619: 2616: 2613: 2527: 2496: 2490: 2463: 2457: 2415: 2405: 2379: 2366: 2336: 2326: 2303: 2285: 2231: 2221: 2160: 2154: 2106: 2098: 2095: 2092: 2081: 2026: 2022: 2004: 2001: 1998: 1984: 1978: 1965: 1962: 1959: 1945: 1933: 1929: 1911: 1908: 1905: 1891: 1885: 1858: 1855: 1852: 1743: 1740: 1737: 1705: 1702: 1699: 1658: 1647: 1644: 1641: 1630: 1601: 1598: 1595: 1581: 1569: 1558: 1555: 1552: 1541: 1529: 1526: 1523: 1509: 1491: 1488: 1485: 1471: 1453: 1450: 1447: 1433: 1398: 1395: 1392: 1375: 1372: 1369: 1293: 1282: 1279: 1276: 1265: 1218: 1215: 1212: 1198: 1186: 1175: 1172: 1169: 1158: 1146: 1143: 1140: 1126: 1108: 1105: 1102: 1088: 1070: 1067: 1064: 1050: 1022: 1019: 1016: 999: 996: 993: 967: 964: 961: 944: 941: 938: 892: 882: 819: 806: 796: 772: 747: 722: 649: 646: 643: 608: 605: 602: 494: 491: 488: 453: 450: 447: 413: 382: 379: 376: 361:To match what we already observe, 325: 322: 319: 287: 284: 281: 207: 204: 201: 170: 167: 164: 14: 12044: 10737:{\displaystyle \mathbf {E} (z,t)} 8927:{\displaystyle \left|z-z'\right|} 4576:traveling at the speed of light. 11652:De Sitter double star experiment 11546: 11444: 11353: 11320: 11287: 11250: 11228: 11115: 11059: 10866: 10845: 10781: 10752: 10715: 10578: 10477: 10419: 10300: 10242: 10209: 10086: 10062: 9831: 9798: 9772: 9749: 9657: 9557: 9506: 9356:curl of the curl vector identity 9038: 8876: 8623: 6796: 6787: 6764: 6755: 6626: 6617: 6459: 6450: 6429: 6420: 6211: 6190: 6105: 6087: 6079: 6041: 6032: 5999: 5990: 5967: 5956: 5890: 5791: 5775: 5743: 5686: 5590: 5572: 5558: 5465: 5451: 5410: 5394: 5376: 5362: 5344: 5336: 5300: 5260: 5222: 5104: 5065: 4949: 4910: 4871: 4630:{\displaystyle \mathbf {E} _{R}} 4617: 4601:{\displaystyle \mathbf {E} _{T}} 4588: 4310: 4273: 4258:{\displaystyle \exp(-i\omega t)} 4199: 4174: 4146: 4124: 4102: 3851:The total field at any position 3799: 3767: 3741: 3654: 3626: 3554: 3523: 3511: 3326: 3314: 3230: 3177: 3146: 3100: 3055: 2975: 2949:{\displaystyle \exp(-i\omega t)} 2871: 2825: 2787: 2731: 2678: 2630: 2607: 2574: 2538: 2504: 2471: 2167: 2086: 2051: 1992: 1953: 1899: 1846: 1731: 1693: 1635: 1589: 1546: 1517: 1479: 1441: 1386: 1363: 1344: 1322: 1270: 1238: 1206: 1163: 1134: 1096: 1058: 1010: 987: 978: 955: 932: 923: 886: 850: 826: 800: 779: 754: 729: 675: 637: 596: 580:{\displaystyle \mathbf {E} _{R}} 567: 520: 482: 441: 407: 370: 313: 275: 251: 195: 158: 7442:{\displaystyle e^{-\epsilon R}} 5522:{\displaystyle k_{0}=\omega /c} 4499:, we obtain the reflected wave 3940: 976: 122: 11878:. Cambridge University Press. 11867: 11824: 11785: 11336: 11324: 11282: 11270: 11048: 10925: 10774: 10756: 10731: 10719: 10669: 10651: 10225: 10213: 10188: 10176: 10078: 10066: 10054:Therefore, the total field is 9964: 9951: 9802: 9780:{\displaystyle {\mathbf {z} }} 9615: 9586: 9442: 9411: 9402: 9371: 9025: 9013: 8659: 8641: 8609: 8597: 8327: 8305: 8279: 8181: 8162: 8140: 8127: 8072: 7951: 7929: 7888: 7866: 7846: 7750: 7728: 7709: 7672: 7650: 7595: 7389: 7279: 7105: 7045: 6591: 6573: 6570: 6567: 6549: 6247: 6229: 6200: 6186: 6141: 6123: 6097: 6083: 5900: 5886: 5801: 5787: 5753: 5739: 5696: 5682: 5582: 5568: 5475: 5461: 5420: 5406: 5386: 5372: 5354: 5340: 5310: 5296: 5270: 5256: 5232: 5218: 5026:but the magnetic Hertz vector 4517: 4511: 4252: 4237: 3889: 3883: 3791: 3785: 3295: 3279: 3201: 3195: 3124: 3118: 2943: 2928: 2900: 2767: 2520: 2493: 2398: 2375: 2322: 2260: 2172: 2151: 1971: 1942: 1782: 1779: 1761: 1755: 1723: 1711: 697: 685: 667: 655: 626: 614: 542: 530: 512: 500: 471: 459: 343: 331: 305: 293: 267: 255: 225: 213: 22:Ewald–Oseen extinction theorem 1: 12028:Eponymous theorems of physics 11657: 1827:{\displaystyle k=\omega /{c}} 432:Therefore in this formalism, 131: 11770:10.1017/CBO9780511803796.019 11724:10.1007/978-3-319-58403-4_19 11235:{\displaystyle \mathbf {P} } 9756:{\displaystyle \mathbf {P} } 8883:{\displaystyle \mathbf {r} } 6981:Then using the substitution 4131:{\displaystyle \mathbf {P} } 4109:{\displaystyle \mathbf {E} } 3561:{\displaystyle \mathbf {a} } 2581:{\displaystyle \mathbf {J} } 1329:{\displaystyle \mathbf {J} } 71:The original light wave, and 7: 11969:10.1103/PhysRevLett.39.1051 11909:American Journal of Physics 11833:American Journal of Physics 11798:American Journal of Physics 4074:We can simplify the above 39: 10: 12049: 11746:Mansuripur, Masud (2009), 8848:is now only a function of 12008:10.1103/PhysRev.135.B1071 11874:Zangwill, Andrew (2013). 5712:The particular solution, 4766:, in the Lorenz gauge as 4492:{\displaystyle \sigma =0} 3137:with particular solution 11949:Physical Review Letters 6541:cylindrical coordinates 4700:electric susceptibility 4116:induces a polarization 65:superposition principle 54:Lorentz–Lorenz equation 11876:Modern Electrodynamics 11626: 11304: 11236: 11212: 11126: 10993: 10874: 10831: 10738: 10699: 10195: 10046: 9812: 9781: 9757: 9735: 9684: 9487: 9348: 9309: 8980: 8979:{\displaystyle z>0} 8954: 8953:{\displaystyle z<0} 8928: 8884: 8862: 8842: 8803: 8562: 8238: 8106: 8051: 8021: 7471: 7443: 7408: 7316: 7206: 7135: 6973: 6649: 6598: 6533: 6508: 6481: 6153: 6063: 5849: 5808: 5760: 5703: 5649: 5543: 5523: 5482: 5430: 5320: 5191: 5160: 5127: 5051: 5020: 4894: 4760: 4719: 4718:{\displaystyle \chi .} 4692: 4691:{\displaystyle z>0} 4666: 4665:{\displaystyle z<0} 4631: 4602: 4570: 4493: 4467: 4466:{\displaystyle z<0} 4441: 4398: 4376: 4321: 4259: 4218: 4182: 4132: 4110: 4088: 4066: 3987: 3954: 3865: 3843: 3726: 3725:{\displaystyle z>0} 3698: 3611: 3610:{\displaystyle z>0} 3582: 3562: 3540: 3496: 3474: 3370: 3345: 3208: 3131: 2950: 2907: 2706: 2663:, using the fact that 2657: 2582: 2558: 2442: 2128: 1868: 1828: 1792: 1673: 1413: 1330: 1308: 1032: 909: 704: 581: 549: 423: 392: 353: 235: 180: 145: 11627: 11305: 11237: 11213: 11127: 10994: 10875: 10832: 10739: 10700: 10196: 10047: 9813: 9782: 9758: 9736: 9685: 9488: 9349: 9310: 8981: 8955: 8929: 8885: 8863: 8843: 8804: 8563: 8239: 8107: 8052: 8022: 7472: 7444: 7409: 7317: 7212:so the limits become 7207: 7136: 6974: 6650: 6599: 6534: 6509: 6482: 6154: 6064: 5850: 5809: 5761: 5704: 5650: 5544: 5524: 5483: 5431: 5321: 5192: 5161: 5128: 5052: 5021: 4895: 4761: 4720: 4693: 4667: 4641:Hertz vector approach 4632: 4603: 4571: 4494: 4468: 4442: 4399: 4377: 4322: 4260: 4219: 4183: 4133: 4111: 4089: 4067: 3988: 3955: 3866: 3844: 3727: 3699: 3612: 3583: 3563: 3541: 3497: 3475: 3371: 3346: 3209: 3132: 2951: 2908: 2707: 2658: 2583: 2559: 2443: 2129: 1869: 1829: 1793: 1674: 1414: 1331: 1309: 1033: 910: 705: 582: 550: 424: 393: 354: 236: 181: 143: 11684:Principles of Optics 11316: 11246: 11224: 11138: 11003: 10887: 10841: 10748: 10711: 10205: 10058: 9822: 9791: 9767: 9745: 9696: 9497: 9362: 9321: 9317:Instead of plugging 8990: 8964: 8938: 8897: 8872: 8852: 8815: 8574: 8248: 8116: 8061: 8033: 7483: 7453: 7420: 7326: 7216: 7145: 6985: 6658: 6608: 6546: 6539:and convert this to 6518: 6493: 6163: 6075: 5863: 5822: 5770: 5716: 5661: 5553: 5533: 5492: 5446: 5440:homogeneous solution 5332: 5201: 5170: 5166:. To do this, split 5139: 5061: 5030: 4906: 4770: 4739: 4706: 4676: 4650: 4612: 4583: 4503: 4477: 4451: 4408: 4388: 4331: 4269: 4228: 4192: 4142: 4120: 4098: 4078: 3996: 3986:{\displaystyle c/n,} 3966: 3875: 3855: 3736: 3710: 3621: 3595: 3572: 3550: 3506: 3486: 3380: 3355: 3220: 3141: 2960: 2919: 2716: 2667: 2592: 2570: 2454: 2144: 1878: 1841: 1802: 1688: 1425: 1340: 1318: 1042: 919: 715: 591: 562: 436: 402: 365: 247: 190: 153: 107:Principles of Optics 12000:1964PhRv..135.1071F 11961:1977PhRvL..39.1051B 11921:1962AmJPh..30..297F 11845:1981AmJPh..49..950W 10972: 10956: 10626: 10610: 10155: 10017: 9200: 8706: 7821: 7638: 7541: 6924: 6859: 6833: 6715: 6684: 6382: 6353: 6287: 5855:which produces the 3648: 3252: 3168: 61:index of refraction 11994:(4B): B1071–1075. 11647:Special relativity 11622: 11617: 11300: 11232: 11208: 11206: 11122: 10989: 10958: 10942: 10870: 10827: 10734: 10695: 10690: 10612: 10596: 10191: 10141: 10042: 10040: 10003: 9808: 9777: 9753: 9731: 9680: 9678: 9483: 9344: 9305: 9300: 9186: 8976: 8950: 8924: 8880: 8858: 8838: 8799: 8692: 8558: 8556: 8286: 8234: 8188: 8134: 8102: 8079: 8047: 8017: 8015: 7853: 7716: 7690: 7603: 7602: 7506: 7467: 7439: 7404: 7312: 7202: 7131: 6969: 6910: 6845: 6816: 6698: 6667: 6645: 6594: 6532:{\displaystyle y'} 6529: 6507:{\displaystyle x'} 6504: 6477: 6365: 6336: 6273: 6149: 6059: 5845: 5804: 5756: 5699: 5645: 5539: 5519: 5478: 5426: 5316: 5187: 5156: 5123: 5047: 5016: 4890: 4756: 4715: 4688: 4662: 4627: 4598: 4566: 4489: 4463: 4437: 4394: 4372: 4317: 4255: 4214: 4178: 4128: 4106: 4084: 4062: 3983: 3950: 3861: 3839: 3722: 3694: 3624: 3607: 3578: 3558: 3536: 3492: 3470: 3369:{\displaystyle k'} 3366: 3341: 3228: 3204: 3144: 3127: 2946: 2903: 2702: 2653: 2578: 2566:Then substituting 2554: 2438: 2436: 2138:Einstein summation 2124: 2122: 1864: 1824: 1788: 1669: 1667: 1409: 1326: 1304: 1302: 1028: 905: 903: 700: 577: 545: 419: 388: 349: 231: 176: 146: 34:Carl Wilhelm Oseen 26:extinction theorem 11955:(17): 1051–1054. 11929:10.1119/1.1941992 11733:978-3-319-58402-7 11538: 11436: 11166: 11112: 11080: 10987: 10641: 10592: 10528: 10496: 10351: 10319: 9949: 9919: 9868: 9805: 9671: 9571: 9259: 9215: 9121: 9087: 8861:{\displaystyle z} 8690: 8549: 8470: 8381: 8271: 8173: 8119: 8064: 8003: 7917: 7838: 7779: 7701: 7587: 7387: 7277: 7200: 6964: 6899: 6811: 6472: 6271: 6054: 5929: 5542:{\displaystyle z} 5118: 4981: 4963: 4885: 4860: 4815: 4435: 4397:{\displaystyle n} 4087:{\displaystyle n} 4060: 4058: 3864:{\displaystyle z} 3581:{\displaystyle z} 3495:{\displaystyle z} 3463: 2765: 2450:Hence we obtain, 2113: 2033: 1940: 1837:Now to solve for 899: 813: 112:Akhlesh Lakhtakia 12040: 12012: 12011: 11982:Filippas, T.A.; 11979: 11973: 11972: 11944: 11933: 11932: 11901: 11890: 11889: 11871: 11865: 11864: 11828: 11822: 11821: 11789: 11783: 11782: 11763: 11743: 11737: 11736: 11711: 11702: 11701: 11671: 11631: 11629: 11628: 11623: 11621: 11618: 11614: 11601: 11600: 11599: 11598: 11594: 11581: 11580: 11555: 11554: 11549: 11543: 11539: 11537: 11523: 11512: 11499: 11498: 11497: 11496: 11492: 11479: 11478: 11453: 11452: 11447: 11441: 11437: 11435: 11424: 11413: 11404: 11403: 11402: 11398: 11385: 11384: 11362: 11361: 11356: 11323: 11309: 11307: 11306: 11301: 11296: 11295: 11290: 11269: 11268: 11253: 11241: 11239: 11238: 11233: 11231: 11217: 11215: 11214: 11209: 11207: 11200: 11199: 11181: 11177: 11176: 11167: 11156: 11131: 11129: 11128: 11123: 11118: 11113: 11111: 11110: 11109: 11093: 11092: 11083: 11081: 11073: 11068: 11067: 11062: 11047: 11046: 11045: 11041: 11028: 11027: 10998: 10996: 10995: 10990: 10988: 10986: 10985: 10984: 10971: 10966: 10955: 10950: 10941: 10924: 10923: 10922: 10918: 10879: 10877: 10876: 10871: 10869: 10861: 10860: 10848: 10836: 10834: 10833: 10828: 10826: 10825: 10824: 10820: 10807: 10806: 10784: 10755: 10743: 10741: 10740: 10735: 10718: 10704: 10702: 10701: 10696: 10694: 10691: 10687: 10674: 10673: 10672: 10642: 10640: 10639: 10638: 10625: 10620: 10609: 10604: 10595: 10593: 10591: 10590: 10581: 10576: 10571: 10570: 10569: 10565: 10552: 10551: 10529: 10527: 10526: 10525: 10509: 10508: 10499: 10497: 10495: 10494: 10493: 10480: 10475: 10470: 10469: 10468: 10464: 10451: 10450: 10428: 10427: 10422: 10411: 10398: 10397: 10396: 10395: 10391: 10378: 10377: 10352: 10350: 10349: 10348: 10332: 10331: 10322: 10320: 10318: 10317: 10316: 10303: 10298: 10293: 10292: 10291: 10287: 10274: 10273: 10251: 10250: 10245: 10212: 10200: 10198: 10197: 10192: 10175: 10174: 10173: 10161: 10154: 10149: 10137: 10136: 10135: 10131: 10118: 10117: 10095: 10094: 10089: 10065: 10051: 10049: 10048: 10043: 10041: 10037: 10036: 10035: 10023: 10016: 10011: 9996: 9992: 9991: 9990: 9978: 9972: 9971: 9950: 9948: 9947: 9935: 9924: 9920: 9918: 9917: 9916: 9903: 9902: 9901: 9900: 9888: 9882: 9881: 9871: 9869: 9867: 9866: 9854: 9842: 9841: 9840: 9834: 9817: 9815: 9814: 9809: 9807: 9806: 9801: 9796: 9786: 9784: 9783: 9778: 9776: 9775: 9762: 9760: 9759: 9754: 9752: 9740: 9738: 9737: 9732: 9724: 9723: 9722: 9710: 9689: 9687: 9686: 9681: 9679: 9672: 9670: 9669: 9660: 9655: 9650: 9649: 9648: 9636: 9630: 9629: 9614: 9613: 9612: 9600: 9576: 9572: 9570: 9569: 9560: 9555: 9550: 9549: 9548: 9542: 9517: 9516: 9515: 9509: 9492: 9490: 9489: 9484: 9479: 9478: 9477: 9476: 9464: 9457: 9456: 9441: 9440: 9439: 9438: 9426: 9401: 9400: 9399: 9398: 9386: 9353: 9351: 9350: 9345: 9343: 9342: 9341: 9329: 9314: 9312: 9311: 9306: 9304: 9303: 9297: 9284: 9283: 9282: 9278: 9277: 9260: 9258: 9257: 9256: 9237: 9232: 9231: 9216: 9214: 9213: 9212: 9199: 9194: 9184: 9183: 9182: 9169: 9162: 9149: 9148: 9147: 9143: 9142: 9122: 9120: 9119: 9118: 9099: 9088: 9086: 9085: 9084: 9075: 9074: 9061: 9060: 9059: 9041: 9035: 9012: 9011: 9010: 8998: 8985: 8983: 8982: 8977: 8959: 8957: 8956: 8951: 8933: 8931: 8930: 8925: 8923: 8919: 8918: 8889: 8887: 8886: 8881: 8879: 8867: 8865: 8864: 8859: 8847: 8845: 8844: 8839: 8837: 8836: 8835: 8823: 8808: 8806: 8805: 8800: 8798: 8797: 8796: 8792: 8791: 8772: 8771: 8754: 8753: 8752: 8748: 8741: 8717: 8705: 8700: 8691: 8689: 8688: 8687: 8678: 8677: 8664: 8663: 8662: 8632: 8631: 8626: 8616: 8596: 8595: 8594: 8582: 8567: 8565: 8564: 8559: 8557: 8550: 8548: 8547: 8538: 8537: 8536: 8535: 8531: 8524: 8510: 8509: 8492: 8475: 8471: 8469: 8468: 8467: 8454: 8453: 8452: 8451: 8447: 8440: 8426: 8425: 8408: 8391: 8387: 8383: 8382: 8380: 8373: 8372: 8359: 8358: 8357: 8356: 8352: 8345: 8344: 8320: 8319: 8299: 8285: 8243: 8241: 8240: 8235: 8227: 8226: 8211: 8210: 8206: 8205: 8187: 8169: 8168: 8155: 8154: 8133: 8111: 8109: 8108: 8103: 8095: 8094: 8078: 8056: 8054: 8053: 8048: 8046: 8026: 8024: 8023: 8018: 8016: 8009: 8005: 8004: 8002: 7995: 7994: 7981: 7980: 7979: 7978: 7974: 7967: 7944: 7943: 7923: 7918: 7916: 7909: 7908: 7895: 7894: 7881: 7880: 7860: 7852: 7825: 7820: 7815: 7814: 7810: 7803: 7789: 7785: 7784: 7780: 7778: 7771: 7770: 7757: 7756: 7743: 7742: 7722: 7715: 7683: 7679: 7678: 7665: 7664: 7637: 7632: 7631: 7627: 7620: 7601: 7574: 7570: 7569: 7565: 7564: 7540: 7535: 7534: 7530: 7523: 7476: 7474: 7473: 7468: 7466: 7448: 7446: 7445: 7440: 7438: 7437: 7413: 7411: 7410: 7405: 7388: 7386: 7385: 7380: 7376: 7369: 7352: 7351: 7342: 7321: 7319: 7318: 7313: 7311: 7307: 7300: 7278: 7276: 7275: 7270: 7266: 7259: 7242: 7241: 7232: 7211: 7209: 7208: 7203: 7201: 7199: 7198: 7193: 7189: 7182: 7165: 7164: 7155: 7140: 7138: 7137: 7132: 7104: 7103: 7098: 7094: 7087: 7070: 7069: 7057: 7056: 7044: 7043: 7038: 7034: 7027: 7010: 7009: 6997: 6996: 6978: 6976: 6975: 6970: 6965: 6960: 6959: 6955: 6954: 6937: 6935: 6923: 6918: 6900: 6895: 6894: 6890: 6889: 6872: 6870: 6858: 6853: 6844: 6832: 6824: 6812: 6810: 6806: 6805: 6804: 6799: 6790: 6780: 6779: 6778: 6774: 6773: 6772: 6767: 6758: 6748: 6747: 6730: 6728: 6727: 6714: 6709: 6697: 6696: 6683: 6678: 6654: 6652: 6651: 6646: 6638: 6634: 6633: 6629: 6620: 6603: 6601: 6600: 6595: 6538: 6536: 6535: 6530: 6528: 6513: 6511: 6510: 6505: 6503: 6486: 6484: 6483: 6478: 6473: 6471: 6467: 6466: 6462: 6453: 6443: 6442: 6441: 6437: 6436: 6432: 6423: 6413: 6412: 6395: 6393: 6381: 6376: 6364: 6352: 6347: 6335: 6334: 6333: 6329: 6322: 6298: 6286: 6281: 6272: 6270: 6269: 6268: 6252: 6251: 6250: 6220: 6219: 6214: 6207: 6193: 6185: 6184: 6183: 6171: 6158: 6156: 6155: 6150: 6145: 6144: 6114: 6113: 6108: 6090: 6082: 6068: 6066: 6065: 6060: 6055: 6053: 6049: 6048: 6044: 6035: 6025: 6024: 6020: 6016: 6011: 6007: 6006: 6002: 5993: 5974: 5970: 5959: 5953: 5951: 5943: 5942: 5930: 5928: 5927: 5926: 5907: 5893: 5885: 5884: 5883: 5871: 5854: 5852: 5851: 5846: 5844: 5843: 5842: 5830: 5816:Green's function 5813: 5811: 5810: 5805: 5794: 5786: 5785: 5784: 5778: 5765: 5763: 5762: 5757: 5746: 5738: 5737: 5736: 5724: 5708: 5706: 5705: 5700: 5689: 5681: 5680: 5669: 5654: 5652: 5651: 5646: 5641: 5640: 5639: 5635: 5622: 5621: 5599: 5598: 5593: 5575: 5567: 5566: 5561: 5548: 5546: 5545: 5540: 5529:in the positive 5528: 5526: 5525: 5520: 5515: 5504: 5503: 5487: 5485: 5484: 5479: 5468: 5460: 5459: 5454: 5435: 5433: 5432: 5427: 5413: 5405: 5404: 5403: 5397: 5379: 5371: 5370: 5365: 5347: 5339: 5325: 5323: 5322: 5317: 5303: 5295: 5294: 5293: 5281: 5263: 5255: 5254: 5243: 5225: 5217: 5216: 5215: 5209: 5196: 5194: 5193: 5188: 5186: 5185: 5184: 5178: 5165: 5163: 5162: 5157: 5155: 5154: 5153: 5147: 5132: 5130: 5129: 5124: 5119: 5117: 5116: 5107: 5102: 5097: 5096: 5095: 5089: 5068: 5056: 5054: 5053: 5048: 5046: 5045: 5044: 5038: 5025: 5023: 5022: 5017: 5012: 5008: 5007: 5006: 5005: 4999: 4982: 4980: 4969: 4964: 4962: 4961: 4952: 4947: 4942: 4941: 4940: 4934: 4913: 4899: 4897: 4896: 4891: 4886: 4884: 4883: 4874: 4869: 4861: 4859: 4858: 4857: 4844: 4843: 4842: 4841: 4835: 4829: 4828: 4818: 4816: 4814: 4813: 4801: 4796: 4795: 4794: 4788: 4782: 4781: 4765: 4763: 4762: 4757: 4755: 4754: 4753: 4747: 4724: 4722: 4721: 4716: 4697: 4695: 4694: 4689: 4671: 4669: 4668: 4663: 4636: 4634: 4633: 4628: 4626: 4625: 4620: 4607: 4605: 4604: 4599: 4597: 4596: 4591: 4575: 4573: 4572: 4567: 4562: 4558: 4534: 4533: 4528: 4510: 4498: 4496: 4495: 4490: 4472: 4470: 4469: 4464: 4446: 4444: 4443: 4438: 4436: 4434: 4433: 4418: 4403: 4401: 4400: 4395: 4381: 4379: 4378: 4373: 4368: 4367: 4355: 4354: 4326: 4324: 4323: 4318: 4313: 4308: 4307: 4295: 4294: 4276: 4264: 4262: 4261: 4256: 4223: 4221: 4220: 4215: 4207: 4202: 4187: 4185: 4184: 4179: 4177: 4172: 4171: 4162: 4161: 4149: 4137: 4135: 4134: 4129: 4127: 4115: 4113: 4112: 4107: 4105: 4093: 4091: 4090: 4085: 4071: 4069: 4068: 4063: 4061: 4059: 4057: 4053: 4052: 4039: 4028: 4020: 4015: 3992: 3990: 3989: 3984: 3976: 3959: 3957: 3956: 3951: 3936: 3932: 3928: 3906: 3905: 3900: 3882: 3870: 3868: 3867: 3862: 3848: 3846: 3845: 3840: 3838: 3834: 3830: 3808: 3807: 3802: 3784: 3783: 3782: 3770: 3758: 3757: 3756: 3744: 3731: 3729: 3728: 3723: 3703: 3701: 3700: 3695: 3693: 3689: 3685: 3663: 3662: 3657: 3647: 3642: 3641: 3629: 3616: 3614: 3613: 3608: 3587: 3585: 3584: 3579: 3567: 3565: 3564: 3559: 3557: 3545: 3543: 3542: 3537: 3526: 3518: 3514: 3501: 3499: 3498: 3493: 3479: 3477: 3476: 3471: 3469: 3465: 3464: 3462: 3458: 3457: 3444: 3428: 3427: 3418: 3417: 3408: 3407: 3395: 3394: 3375: 3373: 3372: 3367: 3365: 3350: 3348: 3347: 3342: 3334: 3330: 3329: 3321: 3317: 3294: 3286: 3278: 3277: 3262: 3261: 3256: 3251: 3246: 3245: 3233: 3213: 3211: 3210: 3205: 3194: 3193: 3192: 3180: 3167: 3162: 3161: 3149: 3136: 3134: 3133: 3128: 3117: 3116: 3115: 3103: 3091: 3090: 3072: 3071: 3070: 3058: 3052: 3048: 3044: 3030: 3029: 3015: 3014: 3005: 3004: 2992: 2991: 2990: 2978: 2972: 2971: 2955: 2953: 2952: 2947: 2912: 2910: 2909: 2904: 2893: 2888: 2887: 2886: 2874: 2865: 2864: 2855: 2854: 2842: 2841: 2840: 2828: 2822: 2817: 2816: 2804: 2803: 2802: 2790: 2784: 2779: 2778: 2766: 2764: 2753: 2748: 2747: 2746: 2734: 2728: 2727: 2711: 2709: 2708: 2703: 2695: 2694: 2693: 2681: 2662: 2660: 2659: 2654: 2652: 2648: 2647: 2646: 2645: 2633: 2624: 2623: 2622: 2610: 2599: 2587: 2585: 2584: 2579: 2577: 2563: 2561: 2560: 2555: 2553: 2552: 2541: 2535: 2534: 2519: 2518: 2507: 2486: 2485: 2474: 2447: 2445: 2444: 2439: 2437: 2433: 2432: 2423: 2422: 2413: 2412: 2397: 2396: 2387: 2386: 2374: 2373: 2358: 2354: 2353: 2344: 2343: 2334: 2333: 2321: 2320: 2308: 2307: 2306: 2290: 2289: 2288: 2275: 2274: 2253: 2249: 2248: 2239: 2238: 2229: 2228: 2219: 2218: 2203: 2202: 2180: 2179: 2170: 2133: 2131: 2130: 2125: 2123: 2119: 2115: 2114: 2112: 2104: 2103: 2102: 2101: 2089: 2079: 2077: 2076: 2067: 2066: 2054: 2049: 2048: 2034: 2032: 2021: 2009: 2008: 2007: 1995: 1970: 1969: 1968: 1956: 1941: 1939: 1928: 1916: 1915: 1914: 1902: 1873: 1871: 1870: 1865: 1863: 1862: 1861: 1849: 1833: 1831: 1830: 1825: 1823: 1818: 1797: 1795: 1794: 1789: 1748: 1747: 1746: 1734: 1710: 1709: 1708: 1696: 1678: 1676: 1675: 1670: 1668: 1664: 1657: 1652: 1651: 1650: 1638: 1629: 1628: 1619: 1618: 1606: 1605: 1604: 1592: 1575: 1568: 1563: 1562: 1561: 1549: 1534: 1533: 1532: 1520: 1503: 1496: 1495: 1494: 1482: 1465: 1458: 1457: 1456: 1444: 1418: 1416: 1415: 1410: 1408: 1404: 1403: 1402: 1401: 1389: 1380: 1379: 1378: 1366: 1355: 1347: 1335: 1333: 1332: 1327: 1325: 1313: 1311: 1310: 1305: 1303: 1299: 1292: 1287: 1286: 1285: 1273: 1264: 1263: 1254: 1253: 1241: 1236: 1235: 1223: 1222: 1221: 1209: 1192: 1185: 1180: 1179: 1178: 1166: 1151: 1150: 1149: 1137: 1120: 1113: 1112: 1111: 1099: 1082: 1075: 1074: 1073: 1061: 1037: 1035: 1034: 1029: 1027: 1026: 1025: 1013: 1004: 1003: 1002: 990: 981: 972: 971: 970: 958: 949: 948: 947: 935: 926: 914: 912: 911: 906: 904: 900: 898: 890: 889: 880: 878: 877: 872: 866: 865: 853: 848: 847: 842: 829: 814: 812: 804: 803: 794: 782: 757: 732: 709: 707: 706: 701: 684: 683: 678: 654: 653: 652: 640: 613: 612: 611: 599: 586: 584: 583: 578: 576: 575: 570: 554: 552: 551: 546: 529: 528: 523: 499: 498: 497: 485: 458: 457: 456: 444: 428: 426: 425: 420: 418: 417: 416: 410: 397: 395: 394: 389: 387: 386: 385: 373: 358: 356: 355: 350: 330: 329: 328: 316: 292: 291: 290: 278: 254: 240: 238: 237: 232: 212: 211: 210: 198: 185: 183: 182: 177: 175: 174: 173: 161: 80:dipole radiation 50:refractive index 30:Paul Peter Ewald 12048: 12047: 12043: 12042: 12041: 12039: 12038: 12037: 12018: 12017: 12016: 12015: 11988:Physical Review 11980: 11976: 11945: 11936: 11902: 11893: 11886: 11872: 11868: 11853:10.1119/1.12596 11839:(10): 950–953. 11829: 11825: 11810:10.1119/1.19330 11790: 11786: 11780: 11744: 11740: 11734: 11712: 11705: 11699: 11672: 11665: 11660: 11640: 11616: 11615: 11604: 11602: 11576: 11572: 11568: 11564: 11560: 11556: 11550: 11545: 11544: 11527: 11522: 11518: 11517: 11514: 11513: 11502: 11500: 11474: 11470: 11469: 11465: 11458: 11454: 11448: 11443: 11442: 11425: 11414: 11412: 11408: 11380: 11376: 11375: 11371: 11367: 11363: 11357: 11352: 11351: 11350: 11346: 11342: 11319: 11317: 11314: 11313: 11291: 11286: 11285: 11264: 11260: 11249: 11247: 11244: 11243: 11227: 11225: 11222: 11221: 11205: 11204: 11195: 11191: 11179: 11178: 11172: 11168: 11155: 11148: 11141: 11139: 11136: 11135: 11114: 11105: 11101: 11094: 11088: 11084: 11082: 11072: 11063: 11058: 11057: 11023: 11019: 11018: 11014: 11010: 11006: 11004: 11001: 11000: 10980: 10976: 10967: 10962: 10957: 10951: 10946: 10940: 10902: 10898: 10894: 10890: 10888: 10885: 10884: 10865: 10856: 10852: 10844: 10842: 10839: 10838: 10802: 10798: 10797: 10793: 10789: 10785: 10780: 10751: 10749: 10746: 10745: 10714: 10712: 10709: 10708: 10689: 10688: 10677: 10675: 10647: 10643: 10634: 10630: 10621: 10616: 10611: 10605: 10600: 10594: 10586: 10582: 10577: 10575: 10547: 10543: 10542: 10538: 10534: 10530: 10521: 10517: 10510: 10504: 10500: 10498: 10489: 10485: 10481: 10476: 10474: 10446: 10442: 10441: 10437: 10433: 10429: 10423: 10418: 10417: 10416: 10413: 10412: 10401: 10399: 10373: 10369: 10368: 10364: 10357: 10353: 10344: 10340: 10333: 10327: 10323: 10321: 10312: 10308: 10304: 10299: 10297: 10269: 10265: 10264: 10260: 10256: 10252: 10246: 10241: 10240: 10239: 10235: 10231: 10208: 10206: 10203: 10202: 10201:which becomes, 10163: 10162: 10157: 10156: 10150: 10145: 10113: 10109: 10108: 10104: 10100: 10096: 10090: 10085: 10084: 10061: 10059: 10056: 10055: 10039: 10038: 10025: 10024: 10019: 10018: 10012: 10007: 9994: 9993: 9980: 9979: 9974: 9973: 9967: 9963: 9943: 9939: 9934: 9922: 9921: 9912: 9908: 9904: 9890: 9889: 9884: 9883: 9877: 9873: 9872: 9870: 9862: 9858: 9853: 9843: 9836: 9835: 9830: 9829: 9825: 9823: 9820: 9819: 9797: 9795: 9794: 9792: 9789: 9788: 9771: 9770: 9768: 9765: 9764: 9748: 9746: 9743: 9742: 9712: 9711: 9706: 9705: 9697: 9694: 9693: 9677: 9676: 9665: 9661: 9656: 9654: 9638: 9637: 9632: 9631: 9625: 9621: 9602: 9601: 9596: 9595: 9574: 9573: 9565: 9561: 9556: 9554: 9544: 9543: 9538: 9537: 9518: 9511: 9510: 9505: 9504: 9500: 9498: 9495: 9494: 9466: 9465: 9460: 9459: 9458: 9452: 9448: 9428: 9427: 9422: 9421: 9420: 9388: 9387: 9382: 9381: 9380: 9363: 9360: 9359: 9331: 9330: 9325: 9324: 9322: 9319: 9318: 9299: 9298: 9287: 9285: 9273: 9269: 9265: 9261: 9252: 9248: 9241: 9236: 9221: 9217: 9208: 9204: 9195: 9190: 9185: 9178: 9174: 9170: 9168: 9167: 9164: 9163: 9152: 9150: 9138: 9134: 9127: 9123: 9114: 9110: 9103: 9098: 9097: 9090: 9089: 9080: 9076: 9070: 9066: 9062: 9046: 9042: 9037: 9036: 9034: 9000: 8999: 8994: 8993: 8991: 8988: 8987: 8965: 8962: 8961: 8939: 8936: 8935: 8911: 8904: 8900: 8898: 8895: 8894: 8875: 8873: 8870: 8869: 8853: 8850: 8849: 8825: 8824: 8819: 8818: 8816: 8813: 8812: 8784: 8777: 8773: 8767: 8763: 8759: 8755: 8734: 8733: 8729: 8722: 8718: 8710: 8701: 8696: 8683: 8679: 8673: 8669: 8665: 8637: 8633: 8627: 8622: 8621: 8617: 8615: 8584: 8583: 8578: 8577: 8575: 8572: 8571: 8555: 8554: 8543: 8539: 8517: 8516: 8512: 8511: 8505: 8501: 8497: 8493: 8491: 8473: 8472: 8463: 8459: 8455: 8433: 8432: 8428: 8427: 8421: 8417: 8413: 8409: 8407: 8389: 8388: 8368: 8364: 8360: 8340: 8336: 8335: 8331: 8330: 8315: 8311: 8304: 8300: 8298: 8291: 8287: 8275: 8258: 8251: 8249: 8246: 8245: 8216: 8212: 8201: 8197: 8193: 8189: 8177: 8150: 8146: 8139: 8135: 8123: 8117: 8114: 8113: 8084: 8080: 8068: 8062: 8059: 8058: 8042: 8034: 8031: 8030: 8014: 8013: 7990: 7986: 7982: 7960: 7959: 7955: 7954: 7939: 7935: 7928: 7924: 7922: 7904: 7900: 7896: 7876: 7872: 7865: 7861: 7859: 7858: 7854: 7842: 7823: 7822: 7816: 7796: 7795: 7791: 7790: 7766: 7762: 7758: 7738: 7734: 7727: 7723: 7721: 7717: 7705: 7694: 7691: 7681: 7680: 7660: 7656: 7649: 7645: 7633: 7613: 7612: 7608: 7607: 7591: 7572: 7571: 7560: 7556: 7552: 7548: 7536: 7516: 7515: 7511: 7510: 7493: 7486: 7484: 7481: 7480: 7462: 7454: 7451: 7450: 7427: 7423: 7421: 7418: 7417: 7381: 7362: 7361: 7357: 7356: 7347: 7343: 7341: 7327: 7324: 7323: 7293: 7292: 7288: 7271: 7252: 7251: 7247: 7246: 7237: 7233: 7231: 7217: 7214: 7213: 7194: 7175: 7174: 7170: 7169: 7160: 7156: 7154: 7146: 7143: 7142: 7099: 7080: 7079: 7075: 7074: 7065: 7061: 7052: 7048: 7039: 7020: 7019: 7015: 7014: 7005: 7001: 6992: 6988: 6986: 6983: 6982: 6950: 6946: 6942: 6938: 6936: 6928: 6919: 6914: 6885: 6881: 6877: 6873: 6871: 6863: 6854: 6849: 6837: 6825: 6820: 6800: 6795: 6794: 6786: 6785: 6781: 6768: 6763: 6762: 6754: 6753: 6749: 6743: 6739: 6735: 6731: 6729: 6723: 6719: 6710: 6702: 6692: 6688: 6679: 6671: 6659: 6656: 6655: 6625: 6624: 6616: 6615: 6611: 6609: 6606: 6605: 6547: 6544: 6543: 6521: 6519: 6516: 6515: 6496: 6494: 6491: 6490: 6458: 6457: 6449: 6448: 6444: 6428: 6427: 6419: 6418: 6414: 6408: 6404: 6400: 6396: 6394: 6386: 6377: 6369: 6357: 6348: 6340: 6315: 6314: 6310: 6303: 6299: 6291: 6282: 6277: 6264: 6260: 6253: 6225: 6221: 6215: 6210: 6209: 6208: 6206: 6189: 6173: 6172: 6167: 6166: 6164: 6161: 6160: 6119: 6115: 6109: 6104: 6103: 6086: 6078: 6076: 6073: 6072: 6040: 6039: 6031: 6030: 6026: 6012: 5998: 5997: 5989: 5988: 5984: 5966: 5965: 5964: 5960: 5955: 5954: 5952: 5944: 5938: 5934: 5922: 5918: 5911: 5906: 5889: 5873: 5872: 5867: 5866: 5864: 5861: 5860: 5832: 5831: 5826: 5825: 5823: 5820: 5819: 5790: 5780: 5779: 5774: 5773: 5771: 5768: 5767: 5766:and therefore, 5742: 5726: 5725: 5720: 5719: 5717: 5714: 5713: 5685: 5670: 5665: 5664: 5662: 5659: 5658: 5617: 5613: 5612: 5608: 5604: 5600: 5594: 5589: 5588: 5571: 5562: 5557: 5556: 5554: 5551: 5550: 5534: 5531: 5530: 5511: 5499: 5495: 5493: 5490: 5489: 5464: 5455: 5450: 5449: 5447: 5444: 5443: 5409: 5399: 5398: 5393: 5392: 5375: 5366: 5361: 5360: 5343: 5335: 5333: 5330: 5329: 5299: 5283: 5282: 5277: 5276: 5259: 5244: 5239: 5238: 5221: 5211: 5210: 5205: 5204: 5202: 5199: 5198: 5180: 5179: 5174: 5173: 5171: 5168: 5167: 5149: 5148: 5143: 5142: 5140: 5137: 5136: 5112: 5108: 5103: 5101: 5091: 5090: 5085: 5084: 5064: 5062: 5059: 5058: 5040: 5039: 5034: 5033: 5031: 5028: 5027: 5001: 5000: 4995: 4994: 4987: 4983: 4973: 4968: 4957: 4953: 4948: 4946: 4936: 4935: 4930: 4929: 4909: 4907: 4904: 4903: 4879: 4875: 4870: 4868: 4853: 4849: 4845: 4837: 4836: 4831: 4830: 4824: 4820: 4819: 4817: 4809: 4805: 4800: 4790: 4789: 4784: 4783: 4777: 4773: 4771: 4768: 4767: 4749: 4748: 4743: 4742: 4740: 4737: 4736: 4733:Hertz Potential 4707: 4704: 4703: 4677: 4674: 4673: 4651: 4648: 4647: 4643: 4621: 4616: 4615: 4613: 4610: 4609: 4592: 4587: 4586: 4584: 4581: 4580: 4545: 4541: 4529: 4524: 4523: 4506: 4504: 4501: 4500: 4478: 4475: 4474: 4452: 4449: 4448: 4429: 4425: 4417: 4409: 4406: 4405: 4389: 4386: 4385: 4363: 4359: 4350: 4346: 4332: 4329: 4328: 4309: 4303: 4299: 4290: 4286: 4272: 4270: 4267: 4266: 4229: 4226: 4225: 4203: 4198: 4193: 4190: 4189: 4173: 4167: 4163: 4157: 4153: 4145: 4143: 4140: 4139: 4123: 4121: 4118: 4117: 4101: 4099: 4096: 4095: 4079: 4076: 4075: 4048: 4044: 4043: 4038: 4027: 4016: 4008: 3997: 3994: 3993: 3972: 3967: 3964: 3963: 3921: 3917: 3913: 3901: 3896: 3895: 3878: 3876: 3873: 3872: 3856: 3853: 3852: 3823: 3819: 3815: 3803: 3798: 3797: 3772: 3771: 3766: 3765: 3746: 3745: 3740: 3739: 3737: 3734: 3733: 3711: 3708: 3707: 3678: 3674: 3670: 3658: 3653: 3652: 3643: 3631: 3630: 3625: 3622: 3619: 3618: 3596: 3593: 3592: 3573: 3570: 3569: 3553: 3551: 3548: 3547: 3522: 3510: 3509: 3507: 3504: 3503: 3487: 3484: 3483: 3453: 3449: 3448: 3443: 3433: 3429: 3423: 3419: 3413: 3409: 3403: 3399: 3387: 3383: 3381: 3378: 3377: 3358: 3356: 3353: 3352: 3325: 3313: 3312: 3308: 3304: 3290: 3282: 3273: 3269: 3257: 3247: 3235: 3234: 3229: 3224: 3223: 3221: 3218: 3217: 3182: 3181: 3176: 3175: 3163: 3151: 3150: 3145: 3142: 3139: 3138: 3105: 3104: 3099: 3098: 3086: 3082: 3060: 3059: 3054: 3053: 3040: 3025: 3021: 3020: 3016: 3010: 3006: 3000: 2996: 2980: 2979: 2974: 2973: 2967: 2963: 2961: 2958: 2957: 2920: 2917: 2916: 2889: 2876: 2875: 2870: 2869: 2860: 2856: 2850: 2846: 2830: 2829: 2824: 2823: 2818: 2812: 2808: 2792: 2791: 2786: 2785: 2780: 2774: 2770: 2757: 2752: 2736: 2735: 2730: 2729: 2723: 2719: 2717: 2714: 2713: 2683: 2682: 2677: 2676: 2668: 2665: 2664: 2635: 2634: 2629: 2628: 2612: 2611: 2606: 2605: 2604: 2600: 2595: 2593: 2590: 2589: 2573: 2571: 2568: 2567: 2542: 2537: 2536: 2530: 2526: 2508: 2503: 2502: 2475: 2470: 2469: 2455: 2452: 2451: 2435: 2434: 2428: 2424: 2418: 2414: 2408: 2404: 2392: 2388: 2382: 2378: 2369: 2365: 2356: 2355: 2349: 2345: 2339: 2335: 2329: 2325: 2313: 2309: 2302: 2298: 2294: 2284: 2280: 2276: 2267: 2263: 2251: 2250: 2244: 2240: 2234: 2230: 2224: 2220: 2208: 2204: 2192: 2188: 2181: 2175: 2171: 2166: 2147: 2145: 2142: 2141: 2121: 2120: 2105: 2091: 2090: 2085: 2084: 2080: 2078: 2072: 2068: 2062: 2058: 2050: 2044: 2040: 2039: 2035: 2025: 2020: 2010: 1997: 1996: 1991: 1990: 1975: 1974: 1958: 1957: 1952: 1951: 1932: 1927: 1917: 1904: 1903: 1898: 1897: 1881: 1879: 1876: 1875: 1851: 1850: 1845: 1844: 1842: 1839: 1838: 1819: 1814: 1803: 1800: 1799: 1736: 1735: 1730: 1729: 1698: 1697: 1692: 1691: 1689: 1686: 1685: 1666: 1665: 1653: 1640: 1639: 1634: 1633: 1624: 1620: 1614: 1610: 1594: 1593: 1588: 1587: 1580: 1577: 1576: 1564: 1551: 1550: 1545: 1544: 1522: 1521: 1516: 1515: 1508: 1505: 1504: 1484: 1483: 1478: 1477: 1470: 1467: 1466: 1446: 1445: 1440: 1439: 1432: 1428: 1426: 1423: 1422: 1391: 1390: 1385: 1384: 1368: 1367: 1362: 1361: 1360: 1356: 1351: 1343: 1341: 1338: 1337: 1321: 1319: 1316: 1315: 1301: 1300: 1288: 1275: 1274: 1269: 1268: 1259: 1255: 1249: 1245: 1237: 1231: 1227: 1211: 1210: 1205: 1204: 1197: 1194: 1193: 1181: 1168: 1167: 1162: 1161: 1139: 1138: 1133: 1132: 1125: 1122: 1121: 1101: 1100: 1095: 1094: 1087: 1084: 1083: 1063: 1062: 1057: 1056: 1049: 1045: 1043: 1040: 1039: 1015: 1014: 1009: 1008: 992: 991: 986: 985: 977: 960: 959: 954: 953: 937: 936: 931: 930: 922: 920: 917: 916: 902: 901: 891: 885: 881: 879: 873: 868: 867: 861: 857: 849: 843: 838: 837: 830: 825: 816: 815: 805: 799: 795: 793: 783: 778: 769: 768: 758: 753: 744: 743: 733: 728: 718: 716: 713: 712: 679: 674: 673: 642: 641: 636: 635: 601: 600: 595: 594: 592: 589: 588: 571: 566: 565: 563: 560: 559: 524: 519: 518: 487: 486: 481: 480: 446: 445: 440: 439: 437: 434: 433: 412: 411: 406: 405: 403: 400: 399: 375: 374: 369: 368: 366: 363: 362: 318: 317: 312: 311: 280: 279: 274: 273: 250: 248: 245: 244: 200: 199: 194: 193: 191: 188: 187: 163: 162: 157: 156: 154: 151: 150: 134: 125: 120: 42: 12: 11: 5: 12046: 12036: 12035: 12030: 12014: 12013: 11974: 11934: 11915:(1): 297–300, 11891: 11884: 11866: 11823: 11804:(7): 599–605. 11784: 11778: 11738: 11732: 11703: 11697: 11662: 11661: 11659: 11656: 11639: 11636: 11620: 11613: 11610: 11607: 11603: 11597: 11593: 11590: 11587: 11584: 11579: 11575: 11571: 11567: 11563: 11559: 11553: 11548: 11542: 11536: 11533: 11530: 11526: 11521: 11516: 11515: 11511: 11508: 11505: 11501: 11495: 11491: 11488: 11485: 11482: 11477: 11473: 11468: 11464: 11461: 11457: 11451: 11446: 11440: 11434: 11431: 11428: 11423: 11420: 11417: 11411: 11407: 11401: 11397: 11394: 11391: 11388: 11383: 11379: 11374: 11370: 11366: 11360: 11355: 11349: 11348: 11345: 11341: 11338: 11335: 11332: 11329: 11326: 11322: 11299: 11294: 11289: 11284: 11281: 11278: 11275: 11272: 11267: 11263: 11259: 11256: 11252: 11230: 11203: 11198: 11194: 11190: 11187: 11184: 11182: 11180: 11175: 11171: 11165: 11162: 11159: 11154: 11151: 11149: 11147: 11144: 11143: 11121: 11117: 11108: 11104: 11100: 11097: 11091: 11087: 11079: 11076: 11071: 11066: 11061: 11056: 11053: 11050: 11044: 11040: 11037: 11034: 11031: 11026: 11022: 11017: 11013: 11009: 10983: 10979: 10975: 10970: 10965: 10961: 10954: 10949: 10945: 10939: 10936: 10933: 10930: 10927: 10921: 10917: 10914: 10911: 10908: 10905: 10901: 10897: 10893: 10868: 10864: 10859: 10855: 10851: 10847: 10823: 10819: 10816: 10813: 10810: 10805: 10801: 10796: 10792: 10788: 10783: 10779: 10776: 10773: 10770: 10767: 10764: 10761: 10758: 10754: 10733: 10730: 10727: 10724: 10721: 10717: 10693: 10686: 10683: 10680: 10676: 10671: 10668: 10665: 10662: 10659: 10656: 10653: 10650: 10646: 10637: 10633: 10629: 10624: 10619: 10615: 10608: 10603: 10599: 10589: 10585: 10580: 10574: 10568: 10564: 10561: 10558: 10555: 10550: 10546: 10541: 10537: 10533: 10524: 10520: 10516: 10513: 10507: 10503: 10492: 10488: 10484: 10479: 10473: 10467: 10463: 10460: 10457: 10454: 10449: 10445: 10440: 10436: 10432: 10426: 10421: 10415: 10414: 10410: 10407: 10404: 10400: 10394: 10390: 10387: 10384: 10381: 10376: 10372: 10367: 10363: 10360: 10356: 10347: 10343: 10339: 10336: 10330: 10326: 10315: 10311: 10307: 10302: 10296: 10290: 10286: 10283: 10280: 10277: 10272: 10268: 10263: 10259: 10255: 10249: 10244: 10238: 10237: 10234: 10230: 10227: 10224: 10221: 10218: 10215: 10211: 10190: 10187: 10184: 10181: 10178: 10172: 10169: 10166: 10160: 10153: 10148: 10144: 10140: 10134: 10130: 10127: 10124: 10121: 10116: 10112: 10107: 10103: 10099: 10093: 10088: 10083: 10080: 10077: 10074: 10071: 10068: 10064: 10034: 10031: 10028: 10022: 10015: 10010: 10006: 10002: 9999: 9997: 9995: 9989: 9986: 9983: 9977: 9970: 9966: 9962: 9959: 9956: 9953: 9946: 9942: 9938: 9933: 9930: 9927: 9925: 9923: 9915: 9911: 9907: 9899: 9896: 9893: 9887: 9880: 9876: 9865: 9861: 9857: 9852: 9849: 9846: 9844: 9839: 9833: 9828: 9827: 9804: 9800: 9774: 9751: 9730: 9727: 9721: 9718: 9715: 9709: 9704: 9701: 9675: 9668: 9664: 9659: 9653: 9647: 9644: 9641: 9635: 9628: 9624: 9620: 9617: 9611: 9608: 9605: 9599: 9594: 9591: 9588: 9585: 9582: 9579: 9577: 9575: 9568: 9564: 9559: 9553: 9547: 9541: 9536: 9533: 9530: 9527: 9524: 9521: 9519: 9514: 9508: 9503: 9502: 9482: 9475: 9472: 9469: 9463: 9455: 9451: 9447: 9444: 9437: 9434: 9431: 9425: 9419: 9416: 9413: 9410: 9407: 9404: 9397: 9394: 9391: 9385: 9379: 9376: 9373: 9370: 9367: 9340: 9337: 9334: 9328: 9302: 9296: 9293: 9290: 9286: 9281: 9276: 9272: 9268: 9264: 9255: 9251: 9247: 9244: 9240: 9235: 9230: 9227: 9224: 9220: 9211: 9207: 9203: 9198: 9193: 9189: 9181: 9177: 9173: 9166: 9165: 9161: 9158: 9155: 9151: 9146: 9141: 9137: 9133: 9130: 9126: 9117: 9113: 9109: 9106: 9102: 9096: 9095: 9093: 9083: 9079: 9073: 9069: 9065: 9058: 9055: 9052: 9049: 9045: 9040: 9033: 9030: 9027: 9024: 9021: 9018: 9015: 9009: 9006: 9003: 8997: 8975: 8972: 8969: 8949: 8946: 8943: 8922: 8917: 8914: 8910: 8907: 8903: 8878: 8857: 8834: 8831: 8828: 8822: 8795: 8790: 8787: 8783: 8780: 8776: 8770: 8766: 8762: 8758: 8751: 8747: 8744: 8740: 8737: 8732: 8728: 8725: 8721: 8716: 8713: 8709: 8704: 8699: 8695: 8686: 8682: 8676: 8672: 8668: 8661: 8658: 8655: 8652: 8649: 8646: 8643: 8640: 8636: 8630: 8625: 8620: 8614: 8611: 8608: 8605: 8602: 8599: 8593: 8590: 8587: 8581: 8553: 8546: 8542: 8534: 8530: 8527: 8523: 8520: 8515: 8508: 8504: 8500: 8496: 8490: 8487: 8484: 8481: 8478: 8476: 8474: 8466: 8462: 8458: 8450: 8446: 8443: 8439: 8436: 8431: 8424: 8420: 8416: 8412: 8406: 8403: 8400: 8397: 8394: 8392: 8390: 8386: 8379: 8376: 8371: 8367: 8363: 8355: 8351: 8348: 8343: 8339: 8334: 8329: 8326: 8323: 8318: 8314: 8310: 8307: 8303: 8297: 8294: 8290: 8284: 8281: 8278: 8274: 8270: 8267: 8264: 8261: 8259: 8257: 8254: 8253: 8233: 8230: 8225: 8222: 8219: 8215: 8209: 8204: 8200: 8196: 8192: 8186: 8183: 8180: 8176: 8172: 8167: 8164: 8161: 8158: 8153: 8149: 8145: 8142: 8138: 8132: 8129: 8126: 8122: 8101: 8098: 8093: 8090: 8087: 8083: 8077: 8074: 8071: 8067: 8045: 8041: 8038: 8012: 8008: 8001: 7998: 7993: 7989: 7985: 7977: 7973: 7970: 7966: 7963: 7958: 7953: 7950: 7947: 7942: 7938: 7934: 7931: 7927: 7921: 7915: 7912: 7907: 7903: 7899: 7893: 7890: 7887: 7884: 7879: 7875: 7871: 7868: 7864: 7857: 7851: 7848: 7845: 7841: 7837: 7834: 7831: 7828: 7826: 7824: 7819: 7813: 7809: 7806: 7802: 7799: 7794: 7788: 7783: 7777: 7774: 7769: 7765: 7761: 7755: 7752: 7749: 7746: 7741: 7737: 7733: 7730: 7726: 7720: 7714: 7711: 7708: 7704: 7700: 7697: 7693: 7689: 7686: 7684: 7682: 7677: 7674: 7671: 7668: 7663: 7659: 7655: 7652: 7648: 7644: 7641: 7636: 7630: 7626: 7623: 7619: 7616: 7611: 7606: 7600: 7597: 7594: 7590: 7586: 7583: 7580: 7577: 7575: 7573: 7568: 7563: 7559: 7555: 7551: 7547: 7544: 7539: 7533: 7529: 7526: 7522: 7519: 7514: 7509: 7505: 7502: 7499: 7496: 7494: 7492: 7489: 7488: 7465: 7461: 7458: 7436: 7433: 7430: 7426: 7403: 7400: 7397: 7394: 7391: 7384: 7379: 7375: 7372: 7368: 7365: 7360: 7355: 7350: 7346: 7340: 7337: 7334: 7331: 7310: 7306: 7303: 7299: 7296: 7291: 7287: 7284: 7281: 7274: 7269: 7265: 7262: 7258: 7255: 7250: 7245: 7240: 7236: 7230: 7227: 7224: 7221: 7197: 7192: 7188: 7185: 7181: 7178: 7173: 7168: 7163: 7159: 7153: 7150: 7130: 7127: 7123: 7120: 7117: 7114: 7110: 7107: 7102: 7097: 7093: 7090: 7086: 7083: 7078: 7073: 7068: 7064: 7060: 7055: 7051: 7047: 7042: 7037: 7033: 7030: 7026: 7023: 7018: 7013: 7008: 7004: 7000: 6995: 6991: 6968: 6963: 6958: 6953: 6949: 6945: 6941: 6934: 6931: 6927: 6922: 6917: 6913: 6909: 6906: 6903: 6898: 6893: 6888: 6884: 6880: 6876: 6869: 6866: 6862: 6857: 6852: 6848: 6843: 6840: 6836: 6831: 6828: 6823: 6819: 6815: 6809: 6803: 6798: 6793: 6789: 6784: 6777: 6771: 6766: 6761: 6757: 6752: 6746: 6742: 6738: 6734: 6726: 6722: 6718: 6713: 6708: 6705: 6701: 6695: 6691: 6687: 6682: 6677: 6674: 6670: 6666: 6663: 6644: 6641: 6637: 6632: 6628: 6623: 6619: 6614: 6593: 6590: 6587: 6584: 6581: 6578: 6575: 6572: 6569: 6566: 6563: 6560: 6557: 6554: 6551: 6527: 6524: 6502: 6499: 6476: 6470: 6465: 6461: 6456: 6452: 6447: 6440: 6435: 6431: 6426: 6422: 6417: 6411: 6407: 6403: 6399: 6392: 6389: 6385: 6380: 6375: 6372: 6368: 6363: 6360: 6356: 6351: 6346: 6343: 6339: 6332: 6328: 6325: 6321: 6318: 6313: 6309: 6306: 6302: 6297: 6294: 6290: 6285: 6280: 6276: 6267: 6263: 6259: 6256: 6249: 6246: 6243: 6240: 6237: 6234: 6231: 6228: 6224: 6218: 6213: 6205: 6202: 6199: 6196: 6192: 6188: 6182: 6179: 6176: 6170: 6148: 6143: 6140: 6137: 6134: 6131: 6128: 6125: 6122: 6118: 6112: 6107: 6102: 6099: 6096: 6093: 6089: 6085: 6081: 6058: 6052: 6047: 6043: 6038: 6034: 6029: 6023: 6019: 6015: 6010: 6005: 6001: 5996: 5992: 5987: 5983: 5980: 5977: 5973: 5969: 5963: 5958: 5950: 5947: 5941: 5937: 5933: 5925: 5921: 5917: 5914: 5910: 5905: 5902: 5899: 5896: 5892: 5888: 5882: 5879: 5876: 5870: 5841: 5838: 5835: 5829: 5803: 5800: 5797: 5793: 5789: 5783: 5777: 5755: 5752: 5749: 5745: 5741: 5735: 5732: 5729: 5723: 5698: 5695: 5692: 5688: 5684: 5679: 5676: 5673: 5668: 5644: 5638: 5634: 5631: 5628: 5625: 5620: 5616: 5611: 5607: 5603: 5597: 5592: 5587: 5584: 5581: 5578: 5574: 5570: 5565: 5560: 5538: 5518: 5514: 5510: 5507: 5502: 5498: 5477: 5474: 5471: 5467: 5463: 5458: 5453: 5425: 5422: 5419: 5416: 5412: 5408: 5402: 5396: 5391: 5388: 5385: 5382: 5378: 5374: 5369: 5364: 5359: 5356: 5353: 5350: 5346: 5342: 5338: 5315: 5312: 5309: 5306: 5302: 5298: 5292: 5289: 5286: 5280: 5275: 5272: 5269: 5266: 5262: 5258: 5253: 5250: 5247: 5242: 5237: 5234: 5231: 5228: 5224: 5220: 5214: 5208: 5183: 5177: 5152: 5146: 5122: 5115: 5111: 5106: 5100: 5094: 5088: 5083: 5080: 5077: 5074: 5071: 5067: 5043: 5037: 5015: 5011: 5004: 4998: 4993: 4990: 4986: 4979: 4976: 4972: 4967: 4960: 4956: 4951: 4945: 4939: 4933: 4928: 4925: 4922: 4919: 4916: 4912: 4889: 4882: 4878: 4873: 4867: 4864: 4856: 4852: 4848: 4840: 4834: 4827: 4823: 4812: 4808: 4804: 4799: 4793: 4787: 4780: 4776: 4752: 4746: 4714: 4711: 4687: 4684: 4681: 4661: 4658: 4655: 4642: 4639: 4624: 4619: 4595: 4590: 4565: 4561: 4557: 4554: 4551: 4548: 4544: 4540: 4537: 4532: 4527: 4522: 4519: 4516: 4513: 4509: 4488: 4485: 4482: 4462: 4459: 4456: 4432: 4428: 4424: 4421: 4416: 4413: 4393: 4371: 4366: 4362: 4358: 4353: 4349: 4345: 4342: 4339: 4336: 4316: 4312: 4306: 4302: 4298: 4293: 4289: 4285: 4282: 4279: 4275: 4254: 4251: 4248: 4245: 4242: 4239: 4236: 4233: 4213: 4210: 4206: 4201: 4197: 4176: 4170: 4166: 4160: 4156: 4152: 4148: 4126: 4104: 4083: 4056: 4051: 4047: 4042: 4037: 4034: 4031: 4026: 4023: 4019: 4014: 4011: 4007: 4004: 4001: 3982: 3979: 3975: 3971: 3949: 3946: 3943: 3939: 3935: 3931: 3927: 3924: 3920: 3916: 3912: 3909: 3904: 3899: 3894: 3891: 3888: 3885: 3881: 3860: 3837: 3833: 3829: 3826: 3822: 3818: 3814: 3811: 3806: 3801: 3796: 3793: 3790: 3787: 3781: 3778: 3775: 3769: 3764: 3761: 3755: 3752: 3749: 3743: 3721: 3718: 3715: 3692: 3688: 3684: 3681: 3677: 3673: 3669: 3666: 3661: 3656: 3651: 3646: 3640: 3637: 3634: 3628: 3606: 3603: 3600: 3577: 3556: 3535: 3532: 3529: 3525: 3521: 3517: 3513: 3491: 3468: 3461: 3456: 3452: 3447: 3442: 3439: 3436: 3432: 3426: 3422: 3416: 3412: 3406: 3402: 3398: 3393: 3390: 3386: 3364: 3361: 3340: 3337: 3333: 3328: 3324: 3320: 3316: 3311: 3307: 3303: 3300: 3297: 3293: 3289: 3285: 3281: 3276: 3272: 3268: 3265: 3260: 3255: 3250: 3244: 3241: 3238: 3232: 3227: 3203: 3200: 3197: 3191: 3188: 3185: 3179: 3174: 3171: 3166: 3160: 3157: 3154: 3148: 3126: 3123: 3120: 3114: 3111: 3108: 3102: 3097: 3094: 3089: 3085: 3081: 3078: 3075: 3069: 3066: 3063: 3057: 3051: 3047: 3043: 3039: 3036: 3033: 3028: 3024: 3019: 3013: 3009: 3003: 2999: 2995: 2989: 2986: 2983: 2977: 2970: 2966: 2945: 2942: 2939: 2936: 2933: 2930: 2927: 2924: 2902: 2899: 2896: 2892: 2885: 2882: 2879: 2873: 2868: 2863: 2859: 2853: 2849: 2845: 2839: 2836: 2833: 2827: 2821: 2815: 2811: 2807: 2801: 2798: 2795: 2789: 2783: 2777: 2773: 2769: 2763: 2760: 2756: 2751: 2745: 2742: 2739: 2733: 2726: 2722: 2701: 2698: 2692: 2689: 2686: 2680: 2675: 2672: 2651: 2644: 2641: 2638: 2632: 2627: 2621: 2618: 2615: 2609: 2603: 2598: 2576: 2551: 2548: 2545: 2540: 2533: 2529: 2525: 2522: 2517: 2514: 2511: 2506: 2501: 2498: 2495: 2492: 2489: 2484: 2481: 2478: 2473: 2468: 2465: 2462: 2459: 2431: 2427: 2421: 2417: 2411: 2407: 2403: 2400: 2395: 2391: 2385: 2381: 2377: 2372: 2368: 2364: 2361: 2359: 2357: 2352: 2348: 2342: 2338: 2332: 2328: 2324: 2319: 2316: 2312: 2305: 2301: 2297: 2293: 2287: 2283: 2279: 2273: 2270: 2266: 2262: 2259: 2256: 2254: 2252: 2247: 2243: 2237: 2233: 2227: 2223: 2217: 2214: 2211: 2207: 2201: 2198: 2195: 2191: 2187: 2184: 2182: 2178: 2174: 2169: 2165: 2162: 2159: 2156: 2153: 2150: 2149: 2118: 2111: 2108: 2100: 2097: 2094: 2088: 2083: 2075: 2071: 2065: 2061: 2057: 2053: 2047: 2043: 2038: 2031: 2028: 2024: 2019: 2016: 2013: 2011: 2006: 2003: 2000: 1994: 1989: 1986: 1983: 1980: 1977: 1976: 1973: 1967: 1964: 1961: 1955: 1950: 1947: 1944: 1938: 1935: 1931: 1926: 1923: 1920: 1918: 1913: 1910: 1907: 1901: 1896: 1893: 1890: 1887: 1884: 1883: 1860: 1857: 1854: 1848: 1822: 1817: 1813: 1810: 1807: 1787: 1784: 1781: 1778: 1775: 1772: 1769: 1766: 1763: 1760: 1757: 1754: 1751: 1745: 1742: 1739: 1733: 1728: 1725: 1722: 1719: 1716: 1713: 1707: 1704: 1701: 1695: 1663: 1660: 1656: 1649: 1646: 1643: 1637: 1632: 1627: 1623: 1617: 1613: 1609: 1603: 1600: 1597: 1591: 1586: 1583: 1579: 1578: 1574: 1571: 1567: 1560: 1557: 1554: 1548: 1543: 1540: 1537: 1531: 1528: 1525: 1519: 1514: 1511: 1507: 1506: 1502: 1499: 1493: 1490: 1487: 1481: 1476: 1473: 1469: 1468: 1464: 1461: 1455: 1452: 1449: 1443: 1438: 1435: 1431: 1430: 1407: 1400: 1397: 1394: 1388: 1383: 1377: 1374: 1371: 1365: 1359: 1354: 1350: 1346: 1324: 1298: 1295: 1291: 1284: 1281: 1278: 1272: 1267: 1262: 1258: 1252: 1248: 1244: 1240: 1234: 1230: 1226: 1220: 1217: 1214: 1208: 1203: 1200: 1196: 1195: 1191: 1188: 1184: 1177: 1174: 1171: 1165: 1160: 1157: 1154: 1148: 1145: 1142: 1136: 1131: 1128: 1124: 1123: 1119: 1116: 1110: 1107: 1104: 1098: 1093: 1090: 1086: 1085: 1081: 1078: 1072: 1069: 1066: 1060: 1055: 1052: 1048: 1047: 1024: 1021: 1018: 1012: 1007: 1001: 998: 995: 989: 984: 980: 975: 969: 966: 963: 957: 952: 946: 943: 940: 934: 929: 925: 897: 894: 888: 884: 876: 871: 864: 860: 856: 852: 846: 841: 836: 833: 831: 828: 824: 821: 818: 817: 811: 808: 802: 798: 792: 789: 786: 784: 781: 777: 774: 771: 770: 767: 764: 761: 759: 756: 752: 749: 746: 745: 742: 739: 736: 734: 731: 727: 724: 721: 720: 699: 696: 693: 690: 687: 682: 677: 672: 669: 666: 663: 660: 657: 651: 648: 645: 639: 634: 631: 628: 625: 622: 619: 616: 610: 607: 604: 598: 574: 569: 544: 541: 538: 535: 532: 527: 522: 517: 514: 511: 508: 505: 502: 496: 493: 490: 484: 479: 476: 473: 470: 467: 464: 461: 455: 452: 449: 443: 415: 409: 384: 381: 378: 372: 348: 345: 342: 339: 336: 333: 327: 324: 321: 315: 310: 307: 304: 301: 298: 295: 289: 286: 283: 277: 272: 269: 266: 263: 260: 257: 253: 230: 227: 224: 221: 218: 215: 209: 206: 203: 197: 172: 169: 166: 160: 133: 130: 124: 121: 119: 116: 76: 75: 72: 41: 38: 9: 6: 4: 3: 2: 12045: 12034: 12031: 12029: 12026: 12025: 12023: 12009: 12005: 12001: 11997: 11993: 11989: 11985: 11978: 11970: 11966: 11962: 11958: 11954: 11950: 11943: 11941: 11939: 11930: 11926: 11922: 11918: 11914: 11910: 11906: 11900: 11898: 11896: 11887: 11885:9780521896979 11881: 11877: 11870: 11862: 11858: 11854: 11850: 11846: 11842: 11838: 11834: 11827: 11819: 11815: 11811: 11807: 11803: 11799: 11795: 11788: 11781: 11779:9780511803796 11775: 11771: 11767: 11762: 11757: 11753: 11749: 11742: 11735: 11729: 11725: 11721: 11717: 11710: 11708: 11700: 11698:9780521784498 11694: 11690: 11686: 11685: 11680: 11676: 11670: 11668: 11663: 11655: 11653: 11648: 11644: 11635: 11632: 11611: 11608: 11605: 11595: 11591: 11588: 11585: 11582: 11577: 11573: 11569: 11565: 11561: 11557: 11551: 11540: 11534: 11531: 11528: 11524: 11519: 11509: 11506: 11503: 11493: 11489: 11486: 11483: 11480: 11475: 11471: 11466: 11462: 11459: 11455: 11449: 11438: 11432: 11429: 11426: 11421: 11418: 11415: 11409: 11405: 11399: 11395: 11392: 11389: 11386: 11381: 11377: 11372: 11368: 11364: 11358: 11343: 11339: 11333: 11330: 11327: 11310: 11297: 11292: 11279: 11276: 11273: 11265: 11261: 11257: 11254: 11218: 11201: 11196: 11192: 11188: 11185: 11183: 11173: 11169: 11163: 11160: 11157: 11152: 11150: 11145: 11132: 11119: 11106: 11102: 11098: 11095: 11089: 11085: 11077: 11074: 11069: 11064: 11054: 11051: 11042: 11038: 11035: 11032: 11029: 11024: 11020: 11015: 11011: 11007: 10981: 10977: 10973: 10968: 10963: 10959: 10952: 10947: 10943: 10937: 10934: 10931: 10928: 10919: 10915: 10912: 10909: 10906: 10903: 10899: 10895: 10891: 10881: 10862: 10857: 10853: 10849: 10821: 10817: 10814: 10811: 10808: 10803: 10799: 10794: 10790: 10786: 10777: 10771: 10768: 10765: 10762: 10759: 10728: 10725: 10722: 10705: 10684: 10681: 10678: 10666: 10663: 10660: 10657: 10654: 10648: 10644: 10635: 10631: 10627: 10622: 10617: 10613: 10606: 10601: 10597: 10587: 10583: 10572: 10566: 10562: 10559: 10556: 10553: 10548: 10544: 10539: 10535: 10531: 10522: 10518: 10514: 10511: 10505: 10501: 10490: 10486: 10482: 10471: 10465: 10461: 10458: 10455: 10452: 10447: 10443: 10438: 10434: 10430: 10424: 10408: 10405: 10402: 10392: 10388: 10385: 10382: 10379: 10374: 10370: 10365: 10361: 10358: 10354: 10345: 10341: 10337: 10334: 10328: 10324: 10313: 10309: 10305: 10294: 10288: 10284: 10281: 10278: 10275: 10270: 10266: 10261: 10257: 10253: 10247: 10232: 10228: 10222: 10219: 10216: 10185: 10182: 10179: 10167: 10151: 10146: 10142: 10138: 10132: 10128: 10125: 10122: 10119: 10114: 10110: 10105: 10101: 10097: 10091: 10081: 10075: 10072: 10069: 10052: 10029: 10013: 10008: 10004: 10000: 9998: 9984: 9968: 9960: 9957: 9954: 9944: 9940: 9936: 9931: 9928: 9926: 9913: 9909: 9894: 9878: 9863: 9859: 9855: 9850: 9847: 9845: 9728: 9725: 9716: 9702: 9690: 9673: 9666: 9662: 9651: 9642: 9626: 9618: 9606: 9592: 9580: 9578: 9566: 9562: 9551: 9534: 9528: 9522: 9520: 9480: 9470: 9453: 9445: 9432: 9417: 9405: 9392: 9377: 9368: 9357: 9335: 9315: 9294: 9291: 9288: 9279: 9274: 9270: 9266: 9262: 9253: 9249: 9245: 9242: 9238: 9233: 9228: 9225: 9222: 9218: 9209: 9205: 9201: 9196: 9191: 9187: 9179: 9175: 9171: 9159: 9156: 9153: 9144: 9139: 9135: 9131: 9128: 9124: 9115: 9111: 9107: 9104: 9100: 9091: 9081: 9077: 9071: 9067: 9063: 9056: 9053: 9050: 9047: 9043: 9031: 9028: 9022: 9019: 9016: 9004: 8973: 8970: 8967: 8947: 8944: 8941: 8920: 8915: 8912: 8908: 8905: 8901: 8891: 8855: 8829: 8809: 8793: 8788: 8785: 8781: 8778: 8774: 8768: 8764: 8760: 8756: 8749: 8745: 8742: 8738: 8735: 8730: 8726: 8723: 8719: 8714: 8711: 8707: 8697: 8693: 8684: 8680: 8674: 8670: 8666: 8656: 8653: 8650: 8647: 8644: 8638: 8634: 8628: 8618: 8612: 8606: 8603: 8600: 8588: 8568: 8551: 8544: 8540: 8532: 8528: 8525: 8521: 8518: 8513: 8506: 8502: 8498: 8494: 8488: 8485: 8482: 8479: 8477: 8464: 8460: 8456: 8448: 8444: 8441: 8437: 8434: 8429: 8422: 8418: 8414: 8410: 8404: 8401: 8398: 8395: 8393: 8384: 8377: 8374: 8369: 8365: 8361: 8353: 8349: 8346: 8337: 8332: 8324: 8321: 8316: 8312: 8308: 8301: 8295: 8292: 8288: 8282: 8276: 8268: 8265: 8262: 8260: 8255: 8244:. Therefore, 8231: 8228: 8220: 8217: 8213: 8202: 8198: 8194: 8190: 8184: 8178: 8170: 8159: 8156: 8151: 8147: 8143: 8136: 8130: 8124: 8099: 8096: 8088: 8085: 8081: 8075: 8069: 8039: 8036: 8027: 8010: 8006: 7999: 7996: 7991: 7987: 7983: 7975: 7971: 7968: 7964: 7961: 7956: 7948: 7945: 7940: 7936: 7932: 7925: 7919: 7913: 7910: 7905: 7901: 7897: 7885: 7882: 7877: 7873: 7869: 7862: 7855: 7849: 7843: 7835: 7832: 7829: 7827: 7811: 7807: 7804: 7800: 7797: 7792: 7786: 7781: 7775: 7772: 7767: 7763: 7759: 7753: 7747: 7744: 7739: 7735: 7731: 7724: 7718: 7712: 7706: 7698: 7695: 7687: 7685: 7675: 7669: 7666: 7661: 7657: 7653: 7646: 7642: 7639: 7628: 7624: 7621: 7617: 7614: 7609: 7604: 7598: 7592: 7584: 7581: 7578: 7576: 7566: 7561: 7557: 7553: 7549: 7545: 7542: 7531: 7527: 7524: 7520: 7517: 7512: 7507: 7503: 7500: 7497: 7495: 7490: 7478: 7459: 7456: 7434: 7431: 7428: 7424: 7414: 7401: 7395: 7392: 7382: 7377: 7373: 7370: 7366: 7363: 7358: 7353: 7348: 7344: 7338: 7332: 7329: 7308: 7304: 7301: 7297: 7294: 7289: 7285: 7282: 7272: 7267: 7263: 7260: 7256: 7253: 7248: 7243: 7238: 7234: 7228: 7225: 7222: 7219: 7195: 7190: 7186: 7183: 7179: 7176: 7171: 7166: 7161: 7157: 7151: 7148: 7128: 7125: 7121: 7118: 7115: 7112: 7108: 7100: 7095: 7091: 7088: 7084: 7081: 7076: 7071: 7066: 7062: 7058: 7053: 7049: 7040: 7035: 7031: 7028: 7024: 7021: 7016: 7011: 7006: 7002: 6998: 6993: 6989: 6979: 6966: 6961: 6956: 6951: 6947: 6943: 6939: 6932: 6929: 6925: 6915: 6911: 6907: 6904: 6901: 6896: 6891: 6886: 6882: 6878: 6874: 6867: 6864: 6860: 6850: 6846: 6841: 6838: 6834: 6829: 6826: 6821: 6817: 6813: 6807: 6791: 6782: 6775: 6759: 6750: 6744: 6740: 6736: 6732: 6720: 6716: 6703: 6699: 6689: 6685: 6672: 6668: 6664: 6661: 6642: 6639: 6635: 6630: 6621: 6612: 6588: 6585: 6582: 6579: 6576: 6564: 6561: 6558: 6555: 6552: 6542: 6525: 6522: 6500: 6497: 6487: 6474: 6468: 6463: 6454: 6445: 6438: 6433: 6424: 6415: 6409: 6405: 6401: 6397: 6390: 6387: 6383: 6370: 6366: 6361: 6358: 6354: 6341: 6337: 6330: 6326: 6323: 6319: 6316: 6311: 6307: 6304: 6300: 6295: 6292: 6288: 6278: 6274: 6265: 6261: 6257: 6254: 6244: 6241: 6238: 6235: 6232: 6226: 6222: 6216: 6203: 6197: 6194: 6177: 6146: 6138: 6135: 6132: 6129: 6126: 6120: 6116: 6110: 6100: 6094: 6091: 6069: 6056: 6050: 6045: 6036: 6027: 6021: 6017: 6013: 6008: 6003: 5994: 5985: 5981: 5978: 5975: 5971: 5961: 5948: 5945: 5939: 5935: 5931: 5923: 5919: 5915: 5912: 5908: 5903: 5897: 5894: 5877: 5858: 5836: 5817: 5798: 5795: 5750: 5747: 5730: 5710: 5693: 5690: 5677: 5674: 5671: 5655: 5642: 5636: 5632: 5629: 5626: 5623: 5618: 5614: 5609: 5605: 5601: 5595: 5585: 5579: 5576: 5563: 5536: 5516: 5512: 5508: 5505: 5500: 5496: 5472: 5469: 5456: 5441: 5436: 5423: 5417: 5414: 5389: 5383: 5380: 5367: 5357: 5351: 5348: 5326: 5313: 5307: 5304: 5287: 5273: 5267: 5264: 5251: 5248: 5245: 5235: 5229: 5226: 5133: 5120: 5113: 5109: 5098: 5081: 5075: 5069: 5013: 5009: 4991: 4984: 4977: 4965: 4958: 4954: 4943: 4926: 4920: 4914: 4900: 4887: 4880: 4876: 4865: 4862: 4854: 4850: 4825: 4810: 4806: 4802: 4797: 4778: 4734: 4730: 4725: 4712: 4709: 4701: 4685: 4682: 4679: 4659: 4656: 4653: 4638: 4622: 4593: 4577: 4563: 4559: 4555: 4552: 4549: 4546: 4542: 4538: 4535: 4530: 4520: 4514: 4486: 4483: 4480: 4460: 4457: 4454: 4430: 4426: 4422: 4419: 4414: 4411: 4391: 4382: 4369: 4364: 4360: 4356: 4351: 4347: 4343: 4340: 4337: 4334: 4314: 4304: 4300: 4296: 4291: 4287: 4283: 4280: 4277: 4249: 4246: 4243: 4240: 4234: 4231: 4211: 4204: 4168: 4164: 4158: 4154: 4150: 4081: 4072: 4054: 4049: 4045: 4040: 4035: 4032: 4029: 4024: 4021: 4017: 4012: 4009: 4005: 4002: 3999: 3980: 3977: 3973: 3969: 3960: 3947: 3944: 3941: 3937: 3933: 3929: 3925: 3922: 3918: 3914: 3910: 3907: 3902: 3892: 3886: 3858: 3849: 3835: 3831: 3827: 3824: 3820: 3816: 3812: 3809: 3804: 3794: 3788: 3762: 3759: 3719: 3716: 3713: 3704: 3690: 3686: 3682: 3679: 3675: 3671: 3667: 3664: 3659: 3649: 3644: 3604: 3601: 3598: 3589: 3575: 3533: 3530: 3527: 3519: 3515: 3489: 3480: 3466: 3459: 3454: 3450: 3445: 3440: 3437: 3434: 3430: 3424: 3420: 3414: 3410: 3404: 3400: 3396: 3391: 3384: 3362: 3359: 3335: 3331: 3322: 3318: 3309: 3305: 3301: 3298: 3287: 3274: 3270: 3266: 3263: 3258: 3253: 3248: 3225: 3214: 3198: 3172: 3169: 3164: 3121: 3095: 3092: 3087: 3083: 3079: 3076: 3073: 3049: 3045: 3041: 3037: 3034: 3031: 3026: 3022: 3017: 3011: 3007: 3001: 2997: 2993: 2968: 2940: 2937: 2934: 2931: 2925: 2922: 2913: 2897: 2890: 2861: 2857: 2851: 2847: 2843: 2819: 2813: 2809: 2805: 2781: 2775: 2771: 2761: 2749: 2724: 2699: 2696: 2673: 2649: 2625: 2601: 2596: 2564: 2549: 2546: 2543: 2531: 2523: 2515: 2512: 2509: 2499: 2487: 2482: 2479: 2476: 2466: 2460: 2448: 2429: 2425: 2419: 2409: 2401: 2393: 2389: 2383: 2370: 2362: 2360: 2350: 2346: 2340: 2330: 2317: 2314: 2310: 2299: 2295: 2291: 2281: 2277: 2271: 2268: 2264: 2257: 2255: 2245: 2241: 2235: 2225: 2215: 2212: 2209: 2205: 2199: 2196: 2193: 2189: 2185: 2183: 2176: 2163: 2157: 2139: 2134: 2116: 2109: 2073: 2069: 2063: 2059: 2055: 2045: 2041: 2036: 2029: 2017: 2014: 2012: 1987: 1981: 1948: 1936: 1924: 1921: 1919: 1894: 1888: 1835: 1820: 1815: 1811: 1808: 1805: 1785: 1776: 1773: 1770: 1767: 1764: 1758: 1752: 1749: 1726: 1720: 1717: 1714: 1682: 1679: 1661: 1654: 1625: 1621: 1615: 1611: 1607: 1584: 1572: 1565: 1538: 1535: 1512: 1500: 1497: 1474: 1462: 1459: 1436: 1419: 1405: 1381: 1357: 1352: 1348: 1296: 1289: 1260: 1256: 1250: 1246: 1242: 1232: 1228: 1224: 1201: 1189: 1182: 1155: 1152: 1129: 1117: 1114: 1091: 1079: 1076: 1053: 1005: 982: 973: 950: 927: 895: 874: 862: 858: 854: 844: 834: 832: 822: 809: 790: 787: 785: 775: 765: 762: 760: 750: 740: 737: 735: 725: 694: 691: 688: 680: 670: 664: 661: 658: 632: 629: 623: 620: 617: 572: 555: 539: 536: 533: 525: 515: 509: 506: 503: 477: 474: 468: 465: 462: 430: 359: 346: 340: 337: 334: 308: 302: 299: 296: 270: 264: 261: 258: 241: 228: 222: 219: 216: 142: 138: 129: 115: 113: 109: 108: 102: 100: 94: 92: 88: 83: 81: 73: 70: 69: 68: 66: 62: 57: 55: 51: 47: 37: 35: 31: 27: 23: 19: 11991: 11987: 11977: 11952: 11948: 11912: 11908: 11875: 11869: 11836: 11832: 11826: 11801: 11797: 11787: 11751: 11741: 11715: 11682: 11645: 11641: 11633: 11311: 11219: 11133: 10882: 10706: 10053: 9692:Notice that 9691: 9316: 8892: 8811:Notice that 8810: 8569: 8028: 7479: 7415: 6980: 6488: 6070: 5711: 5656: 5437: 5327: 5134: 4901: 4726: 4644: 4578: 4383: 4073: 3961: 3850: 3705: 3590: 3502:axis. Hence 3481: 3215: 2914: 2565: 2449: 2135: 1836: 1683: 1680: 1420: 556: 431: 360: 242: 147: 135: 126: 123:Introduction 105: 103: 98: 95: 90: 86: 84: 77: 58: 45: 43: 25: 21: 15: 9493:therefore, 2712:we obtain, 12022:Categories 11761:1507.05234 11679:Wolf, Emil 11658:References 5549:direction 132:Derivation 11984:Fox, J.G. 11905:Fox, J.G. 11861:0002-9505 11818:0002-9505 11675:Born, Max 11589:ω 11586:− 11487:ω 11460:− 11419:− 11406:− 11393:ω 11390:− 11277:− 11262:ϵ 11164:χ 11099:− 11075:χ 11070:− 11049:⇒ 11036:ω 11033:− 10974:− 10938:χ 10935:− 10926:⇒ 10913:ω 10910:− 10863:χ 10854:ϵ 10815:ω 10812:− 10664:ω 10661:− 10628:− 10584:ϵ 10573:− 10560:ω 10557:− 10515:− 10487:ϵ 10472:− 10459:ω 10456:− 10386:ω 10359:− 10310:ϵ 10295:− 10282:ω 10279:− 10159:π 10126:ω 10123:− 10021:π 9976:π 9961:ω 9955:− 9932:− 9906:∂ 9886:π 9875:∂ 9851:− 9803:^ 9708:π 9703:⋅ 9700:∇ 9663:ϵ 9652:− 9634:π 9623:∇ 9619:− 9598:π 9593:⋅ 9590:∇ 9584:∇ 9563:ϵ 9552:− 9540:π 9535:× 9532:∇ 9529:× 9526:∇ 9462:π 9450:∇ 9446:− 9424:π 9418:⋅ 9415:∇ 9409:∇ 9384:π 9378:× 9375:∇ 9369:× 9366:∇ 9327:π 9246:− 9202:− 9129:− 9068:ϵ 9054:ω 9048:− 9032:− 8996:π 8909:− 8821:π 8782:− 8743:− 8703:∞ 8694:∫ 8681:ϵ 8654:ω 8651:− 8580:π 8526:− 8486:π 8442:− 8405:π 8399:− 8378:ϵ 8375:− 8347:− 8342:′ 8325:ϵ 8322:− 8296:− 8280:→ 8277:ϵ 8269:π 8224:∞ 8221:ϵ 8218:− 8208:∞ 8182:→ 8179:ϵ 8166:∞ 8160:ϵ 8157:− 8128:→ 8125:ϵ 8092:∞ 8089:ϵ 8086:− 8073:→ 8070:ϵ 8040:∈ 8037:ϵ 8000:ϵ 7997:− 7969:− 7949:ϵ 7946:− 7920:− 7914:ϵ 7911:− 7892:∞ 7886:ϵ 7883:− 7847:→ 7844:ϵ 7836:π 7818:∞ 7805:− 7776:ϵ 7773:− 7748:ϵ 7745:− 7710:→ 7707:ϵ 7699:π 7670:ϵ 7667:− 7635:∞ 7622:− 7605:∫ 7596:→ 7593:ϵ 7585:π 7538:∞ 7525:− 7508:∫ 7504:π 7460:∈ 7457:ϵ 7432:ϵ 7429:− 7399:∞ 7390:⇒ 7371:− 7354:− 7336:∞ 7330:ρ 7302:− 7280:⇒ 7261:− 7244:− 7220:ρ 7184:− 7167:− 7149:ρ 7116:ρ 7109:ρ 7106:⇒ 7089:− 7072:− 7050:ρ 7046:⇒ 7029:− 7003:ρ 6930:ρ 6921:∞ 6912:∫ 6908:π 6865:ρ 6856:∞ 6847:∫ 6839:φ 6830:π 6818:∫ 6802:′ 6792:− 6770:′ 6760:− 6725:′ 6712:∞ 6707:∞ 6704:− 6700:∫ 6694:′ 6681:∞ 6676:∞ 6673:− 6669:∫ 6622:− 6604:and call 6583:φ 6577:ρ 6571:→ 6455:− 6425:− 6379:∞ 6374:∞ 6371:− 6367:∫ 6350:∞ 6345:∞ 6342:− 6338:∫ 6324:− 6284:∞ 6275:∫ 6262:ϵ 6258:π 6242:ω 6239:− 6169:π 6136:ω 6133:− 6037:− 5995:− 5982:− 5932:∫ 5920:ϵ 5916:π 5869:π 5859:integral 5828:π 5722:π 5667:π 5630:ω 5627:− 5509:ω 5279:π 5241:π 5207:π 5176:π 5145:π 5110:ϵ 5099:− 5087:π 5082:× 5079:∇ 5076:× 5073:∇ 5036:π 4997:π 4992:× 4989:∇ 4975:∂ 4971:∂ 4966:− 4955:ϵ 4944:− 4932:π 4927:× 4924:∇ 4921:× 4918:∇ 4877:ϵ 4866:− 4847:∂ 4833:π 4822:∂ 4798:− 4786:π 4775:∇ 4745:π 4710:χ 4547:− 4539:⁡ 4481:σ 4427:χ 4361:χ 4357:ω 4348:ϵ 4341:− 4335:σ 4301:χ 4297:ω 4288:ϵ 4281:− 4265:, we get 4247:ω 4241:− 4235:⁡ 4209:∂ 4196:∂ 4165:χ 4155:ϵ 4055:ω 4046:ϵ 4041:σ 4022:ω 3911:⁡ 3813:⁡ 3763:− 3668:⁡ 3520:⋅ 3460:ω 3451:ϵ 3446:σ 3421:ω 3411:ϵ 3401:μ 3389:′ 3339:Ω 3323:⋅ 3302:⁡ 3292:ϕ 3284:θ 3267:∫ 3173:− 3096:σ 3093:ω 3084:μ 3077:− 3046:ω 3038:σ 3023:ϵ 3008:ω 2998:μ 2965:∇ 2938:ω 2932:− 2926:⁡ 2895:∂ 2867:∂ 2858:μ 2848:ϵ 2820:σ 2810:μ 2782:σ 2772:μ 2759:∂ 2755:∂ 2721:∇ 2674:⋅ 2671:∇ 2597:σ 2528:∇ 2524:− 2500:⋅ 2497:∇ 2491:∇ 2467:× 2464:∇ 2461:× 2458:∇ 2416:∂ 2406:∂ 2402:− 2380:∂ 2367:∂ 2337:∂ 2327:∂ 2311:δ 2296:δ 2292:− 2278:δ 2265:δ 2232:∂ 2222:∂ 2206:ϵ 2190:ϵ 2164:× 2161:∇ 2158:× 2155:∇ 2107:∂ 2082:∂ 2070:μ 2060:ϵ 2042:μ 2027:∂ 2023:∂ 2018:− 1988:× 1985:∇ 1982:× 1979:∇ 1949:× 1946:∇ 1934:∂ 1930:∂ 1925:− 1895:× 1892:∇ 1889:× 1886:∇ 1812:ω 1774:ω 1771:− 1753:⁡ 1659:∂ 1631:∂ 1622:μ 1612:ϵ 1585:× 1582:∇ 1570:∂ 1542:∂ 1539:− 1513:× 1510:∇ 1475:⋅ 1472:∇ 1437:⋅ 1434:∇ 1353:σ 1294:∂ 1266:∂ 1257:μ 1247:ϵ 1229:μ 1202:× 1199:∇ 1187:∂ 1159:∂ 1156:− 1130:× 1127:∇ 1092:⋅ 1089:∇ 1054:⋅ 1051:∇ 893:∂ 883:∂ 870:μ 859:ϵ 840:μ 823:× 820:∇ 807:∂ 797:∂ 791:− 776:× 773:∇ 751:⋅ 748:∇ 726:⋅ 723:∇ 671:− 633:− 478:− 11681:(1999), 9741:because 8916:′ 8868:and not 8789:′ 8739:′ 8715:′ 8522:′ 8438:′ 8112:, hence 8057:implies 7965:′ 7801:′ 7618:′ 7521:′ 7367:′ 7298:′ 7257:′ 7180:′ 7085:′ 7025:′ 6933:′ 6868:′ 6842:′ 6631:′ 6526:′ 6501:′ 6464:′ 6434:′ 6391:′ 6362:′ 6320:′ 6296:′ 6046:′ 6004:′ 5972:′ 5949:′ 5857:retarded 4404:, gives 4013:′ 3926:′ 3828:′ 3683:′ 3516:′ 3363:′ 3319:′ 40:Overview 11996:Bibcode 11957:Bibcode 11917:Bibcode 11841:Bibcode 9763:has no 56:etc.). 11882: 11859: 11816: 11776: 11730: 11695: 3546:where 3351:where 1314:where 46:derive 20:, the 18:optics 11756:arXiv 8029:Then 7449:with 1798:with 11880:ISBN 11857:ISSN 11814:ISSN 11774:ISBN 11728:ISBN 11693:ISBN 11609:> 11507:< 10999:and 10763:> 10682:> 10406:< 9292:> 9157:< 8971:> 8960:and 8945:< 7322:and 7141:and 6514:and 5438:The 4727:The 4683:> 4657:< 4608:and 4458:< 3945:> 3717:> 3602:> 99:only 91:only 32:and 12004:doi 11992:135 11965:doi 11925:doi 11849:doi 11806:doi 11766:doi 11720:doi 11689:106 8273:lim 8175:lim 8121:lim 8066:lim 7840:lim 7703:lim 7589:lim 4536:exp 4232:exp 3908:exp 3810:exp 3665:exp 3299:exp 2923:exp 2588:by 1750:exp 87:not 82:.) 16:In 12024:: 12002:. 11990:. 11963:. 11953:39 11951:. 11937:^ 11923:, 11913:30 11911:, 11894:^ 11855:. 11847:. 11837:49 11835:. 11812:. 11802:67 11800:. 11796:. 11772:, 11764:, 11750:, 11726:, 11706:^ 11691:, 11677:; 11666:^ 11612:0. 10880:. 10685:0. 9358:, 9295:0. 6665::= 5442:, 4735:, 4702:, 3732:) 3588:. 2140:. 1834:. 114:. 12010:. 12006:: 11998:: 11971:. 11967:: 11959:: 11931:. 11927:: 11919:: 11888:. 11863:. 11851:: 11843:: 11820:. 11808:: 11768:: 11758:: 11722:: 11606:z 11596:) 11592:t 11583:z 11578:0 11574:k 11570:n 11566:( 11562:i 11558:e 11552:0 11547:E 11541:) 11535:1 11532:+ 11529:n 11525:2 11520:( 11510:0 11504:z 11494:) 11490:t 11484:+ 11481:z 11476:0 11472:k 11467:( 11463:i 11456:e 11450:0 11445:E 11439:) 11433:1 11430:+ 11427:n 11422:1 11416:n 11410:( 11400:) 11396:t 11387:z 11382:0 11378:k 11373:( 11369:i 11365:e 11359:0 11354:E 11344:{ 11340:= 11337:) 11334:t 11331:, 11328:z 11325:( 11321:E 11298:. 11293:0 11288:E 11283:) 11280:1 11274:n 11271:( 11266:0 11258:2 11255:= 11251:P 11229:P 11202:. 11197:0 11193:k 11189:n 11186:= 11174:0 11170:k 11161:+ 11158:1 11153:= 11146:k 11120:. 11116:E 11107:0 11103:k 11096:k 11090:0 11086:k 11078:2 11065:0 11060:E 11055:= 11052:0 11043:) 11039:t 11030:z 11025:0 11021:k 11016:( 11012:i 11008:e 10982:2 10978:k 10969:2 10964:0 10960:k 10953:2 10948:0 10944:k 10932:= 10929:1 10920:) 10916:t 10907:z 10904:k 10900:( 10896:i 10892:e 10867:E 10858:0 10850:= 10846:P 10822:) 10818:t 10809:z 10804:0 10800:k 10795:( 10791:i 10787:e 10782:E 10778:= 10775:) 10772:t 10769:, 10766:0 10760:z 10757:( 10753:E 10732:) 10729:t 10726:, 10723:z 10720:( 10716:E 10679:z 10670:) 10667:t 10658:z 10655:k 10652:( 10649:i 10645:e 10636:2 10632:k 10623:2 10618:0 10614:k 10607:2 10602:0 10598:k 10588:0 10579:P 10567:) 10563:t 10554:z 10549:0 10545:k 10540:( 10536:i 10532:e 10523:0 10519:k 10512:k 10506:0 10502:k 10491:0 10483:2 10478:P 10466:) 10462:t 10453:z 10448:0 10444:k 10439:( 10435:i 10431:e 10425:0 10420:E 10409:0 10403:z 10393:) 10389:t 10383:+ 10380:z 10375:0 10371:k 10366:( 10362:i 10355:e 10346:0 10342:k 10338:+ 10335:k 10329:0 10325:k 10314:0 10306:2 10301:P 10289:) 10285:t 10276:z 10271:0 10267:k 10262:( 10258:i 10254:e 10248:0 10243:E 10233:{ 10229:= 10226:) 10223:t 10220:, 10217:z 10214:( 10210:E 10189:) 10186:t 10183:, 10180:z 10177:( 10171:p 10168:, 10165:e 10152:2 10147:0 10143:k 10139:+ 10133:) 10129:t 10120:z 10115:0 10111:k 10106:( 10102:i 10098:e 10092:0 10087:E 10082:= 10079:) 10076:t 10073:, 10070:z 10067:( 10063:E 10033:p 10030:, 10027:e 10014:2 10009:0 10005:k 10001:= 9988:p 9985:, 9982:e 9969:2 9965:) 9958:i 9952:( 9945:2 9941:c 9937:1 9929:= 9914:2 9910:t 9898:p 9895:, 9892:e 9879:2 9864:2 9860:c 9856:1 9848:= 9838:p 9832:E 9799:z 9773:z 9750:P 9729:0 9726:= 9720:p 9717:, 9714:e 9674:. 9667:0 9658:P 9646:p 9643:, 9640:e 9627:2 9616:) 9610:p 9607:, 9604:e 9587:( 9581:= 9567:0 9558:P 9546:e 9523:= 9513:p 9507:E 9481:, 9474:p 9471:, 9468:e 9454:2 9443:) 9436:p 9433:, 9430:e 9412:( 9406:= 9403:) 9396:p 9393:, 9390:e 9372:( 9339:p 9336:, 9333:e 9289:z 9280:z 9275:0 9271:k 9267:i 9263:e 9254:0 9250:k 9243:k 9239:1 9234:+ 9229:z 9226:k 9223:i 9219:e 9210:2 9206:k 9197:2 9192:0 9188:k 9180:0 9176:k 9172:2 9160:0 9154:z 9145:z 9140:0 9136:k 9132:i 9125:e 9116:0 9112:k 9108:+ 9105:k 9101:1 9092:{ 9082:0 9078:k 9072:0 9064:2 9057:t 9051:i 9044:e 9039:P 9029:= 9026:) 9023:t 9020:, 9017:z 9014:( 9008:p 9005:, 9002:e 8974:0 8968:z 8948:0 8942:z 8921:| 8913:z 8906:z 8902:| 8877:r 8856:z 8833:p 8830:, 8827:e 8794:| 8786:z 8779:z 8775:| 8769:0 8765:k 8761:i 8757:e 8750:) 8746:z 8736:z 8731:( 8727:k 8724:i 8720:e 8712:z 8708:d 8698:0 8685:0 8675:0 8671:k 8667:2 8660:) 8657:t 8648:z 8645:k 8642:( 8639:i 8635:e 8629:0 8624:P 8619:i 8613:= 8610:) 8607:t 8604:, 8601:z 8598:( 8592:p 8589:, 8586:e 8552:. 8545:0 8541:k 8533:| 8529:z 8519:z 8514:| 8507:0 8503:k 8499:i 8495:e 8489:i 8483:2 8480:= 8465:0 8461:k 8457:i 8449:| 8445:z 8435:z 8430:| 8423:0 8419:k 8415:i 8411:e 8402:2 8396:= 8385:] 8370:0 8366:k 8362:i 8354:| 8350:z 8338:z 8333:| 8328:) 8317:0 8313:k 8309:i 8306:( 8302:e 8293:0 8289:[ 8283:0 8266:2 8263:= 8256:I 8232:0 8229:= 8214:e 8203:0 8199:k 8195:i 8191:e 8185:0 8171:= 8163:) 8152:0 8148:k 8144:i 8141:( 8137:e 8131:0 8100:0 8097:= 8082:e 8076:0 8044:R 8011:. 8007:] 7992:0 7988:k 7984:i 7976:| 7972:z 7962:z 7957:| 7952:) 7941:0 7937:k 7933:i 7930:( 7926:e 7906:0 7902:k 7898:i 7889:) 7878:0 7874:k 7870:i 7867:( 7863:e 7856:[ 7850:0 7833:2 7830:= 7812:| 7808:z 7798:z 7793:| 7787:| 7782:] 7768:0 7764:k 7760:i 7754:R 7751:) 7740:0 7736:k 7732:i 7729:( 7725:e 7719:[ 7713:0 7696:2 7688:= 7676:R 7673:) 7662:0 7658:k 7654:i 7651:( 7647:e 7643:R 7640:d 7629:| 7625:z 7615:z 7610:| 7599:0 7582:2 7579:= 7567:R 7562:0 7558:k 7554:i 7550:e 7546:R 7543:d 7532:| 7528:z 7518:z 7513:| 7501:2 7498:= 7491:I 7464:R 7435:R 7425:e 7402:. 7396:= 7393:R 7383:2 7378:| 7374:z 7364:z 7359:| 7349:2 7345:R 7339:= 7333:= 7309:| 7305:z 7295:z 7290:| 7286:= 7283:R 7273:2 7268:| 7264:z 7254:z 7249:| 7239:2 7235:R 7229:= 7226:0 7223:= 7196:2 7191:| 7187:z 7177:z 7172:| 7162:2 7158:R 7152:= 7129:R 7126:d 7122:R 7119:= 7113:d 7101:2 7096:| 7092:z 7082:z 7077:| 7067:2 7063:R 7059:= 7054:2 7041:2 7036:| 7032:z 7022:z 7017:| 7012:+ 7007:2 6999:= 6994:2 6990:R 6967:. 6962:R 6957:R 6952:0 6948:k 6944:i 6940:e 6926:d 6916:0 6905:2 6902:= 6897:R 6892:R 6887:0 6883:k 6879:i 6875:e 6861:d 6851:0 6835:d 6827:2 6822:0 6814:= 6808:| 6797:r 6788:r 6783:| 6776:| 6765:r 6756:r 6751:| 6745:0 6741:k 6737:i 6733:e 6721:y 6717:d 6690:x 6686:d 6662:I 6643:R 6640:= 6636:| 6627:r 6618:r 6613:| 6592:) 6589:z 6586:, 6580:, 6574:( 6568:) 6565:z 6562:, 6559:y 6556:, 6553:x 6550:( 6523:y 6498:x 6475:. 6469:| 6460:r 6451:r 6446:| 6439:| 6430:r 6421:r 6416:| 6410:0 6406:k 6402:i 6398:e 6388:y 6384:d 6359:x 6355:d 6331:) 6327:z 6317:z 6312:( 6308:k 6305:i 6301:e 6293:z 6289:d 6279:0 6266:0 6255:4 6248:) 6245:t 6236:z 6233:k 6230:( 6227:i 6223:e 6217:0 6212:P 6204:= 6201:) 6198:t 6195:, 6191:r 6187:( 6181:p 6178:, 6175:e 6147:. 6142:) 6139:t 6130:z 6127:k 6124:( 6121:i 6117:e 6111:0 6106:P 6101:= 6098:) 6095:t 6092:, 6088:r 6084:( 6080:P 6057:. 6051:| 6042:r 6033:r 6028:| 6022:) 6018:c 6014:/ 6009:| 6000:r 5991:r 5986:| 5979:t 5976:, 5968:r 5962:( 5957:P 5946:r 5940:3 5936:d 5924:0 5913:4 5909:1 5904:= 5901:) 5898:t 5895:, 5891:r 5887:( 5881:p 5878:, 5875:e 5840:p 5837:, 5834:e 5802:) 5799:t 5796:, 5792:r 5788:( 5782:p 5776:E 5754:) 5751:t 5748:, 5744:r 5740:( 5734:p 5731:, 5728:e 5697:) 5694:t 5691:, 5687:r 5683:( 5678:h 5675:, 5672:e 5643:. 5637:) 5633:t 5624:z 5619:0 5615:k 5610:( 5606:i 5602:e 5596:0 5591:E 5586:= 5583:) 5580:t 5577:, 5573:r 5569:( 5564:h 5559:E 5537:z 5517:c 5513:/ 5506:= 5501:0 5497:k 5476:) 5473:t 5470:, 5466:r 5462:( 5457:h 5452:E 5424:. 5421:) 5418:t 5415:, 5411:r 5407:( 5401:p 5395:E 5390:+ 5387:) 5384:t 5381:, 5377:r 5373:( 5368:h 5363:E 5358:= 5355:) 5352:t 5349:, 5345:r 5341:( 5337:E 5314:. 5311:) 5308:t 5305:, 5301:r 5297:( 5291:p 5288:, 5285:e 5274:+ 5271:) 5268:t 5265:, 5261:r 5257:( 5252:h 5249:, 5246:e 5236:= 5233:) 5230:t 5227:, 5223:r 5219:( 5213:e 5182:e 5151:e 5121:. 5114:0 5105:P 5093:e 5070:= 5066:E 5042:m 5014:, 5010:) 5003:m 4985:( 4978:t 4959:0 4950:P 4938:e 4915:= 4911:E 4888:. 4881:0 4872:P 4863:= 4855:2 4851:t 4839:e 4826:2 4811:2 4807:c 4803:1 4792:e 4779:2 4751:e 4713:. 4686:0 4680:z 4660:0 4654:z 4623:R 4618:E 4594:T 4589:E 4564:, 4560:) 4556:z 4553:k 4550:i 4543:( 4531:R 4526:E 4521:= 4518:) 4515:z 4512:( 4508:E 4487:0 4484:= 4461:0 4455:z 4431:e 4423:+ 4420:1 4415:= 4412:n 4392:n 4370:. 4365:e 4352:0 4344:i 4338:= 4315:, 4311:E 4305:e 4292:0 4284:i 4278:= 4274:J 4253:) 4250:t 4244:i 4238:( 4212:t 4205:/ 4200:P 4175:E 4169:e 4159:0 4151:= 4147:P 4125:P 4103:E 4082:n 4050:0 4036:i 4033:+ 4030:1 4025:= 4018:/ 4010:k 4006:c 4003:= 4000:n 3981:, 3978:n 3974:/ 3970:c 3948:0 3942:z 3938:, 3934:) 3930:z 3923:k 3919:i 3915:( 3903:T 3898:E 3893:= 3890:) 3887:z 3884:( 3880:E 3859:z 3836:) 3832:z 3825:k 3821:i 3817:( 3805:T 3800:E 3795:+ 3792:) 3789:z 3786:( 3780:c 3777:a 3774:v 3768:E 3760:= 3754:d 3751:a 3748:r 3742:E 3720:0 3714:z 3691:) 3687:z 3680:k 3676:i 3672:( 3660:T 3655:E 3650:= 3645:c 3639:d 3636:a 3633:r 3627:E 3605:0 3599:z 3576:z 3555:a 3534:, 3531:0 3528:= 3524:a 3512:k 3490:z 3467:) 3455:0 3441:i 3438:+ 3435:1 3431:( 3425:2 3415:0 3405:0 3397:= 3392:2 3385:k 3360:k 3336:d 3332:) 3327:r 3315:k 3310:i 3306:( 3296:) 3288:, 3280:( 3275:i 3271:g 3264:= 3259:i 3254:) 3249:c 3243:d 3240:a 3237:r 3231:E 3226:( 3202:) 3199:z 3196:( 3190:c 3187:a 3184:v 3178:E 3170:= 3165:P 3159:d 3156:a 3153:r 3147:E 3125:) 3122:z 3119:( 3113:c 3110:a 3107:v 3101:E 3088:0 3080:i 3074:= 3068:d 3065:a 3062:r 3056:E 3050:) 3042:/ 3035:i 3032:+ 3027:0 3018:( 3012:2 3002:0 2994:+ 2988:d 2985:a 2982:r 2976:E 2969:2 2944:) 2941:t 2935:i 2929:( 2901:) 2898:t 2891:/ 2884:d 2881:a 2878:r 2872:E 2862:0 2852:0 2844:+ 2838:d 2835:a 2832:r 2826:E 2814:0 2806:+ 2800:c 2797:a 2794:v 2788:E 2776:0 2768:( 2762:t 2750:= 2744:d 2741:a 2738:r 2732:E 2725:2 2700:0 2697:= 2691:d 2688:a 2685:r 2679:E 2650:) 2643:d 2640:a 2637:r 2631:E 2626:+ 2620:c 2617:a 2614:v 2608:E 2602:( 2575:J 2550:d 2547:a 2544:r 2539:E 2532:2 2521:) 2516:d 2513:a 2510:r 2505:E 2494:( 2488:= 2483:d 2480:a 2477:r 2472:E 2430:i 2426:E 2420:j 2410:j 2399:) 2394:j 2390:E 2384:j 2376:( 2371:i 2363:= 2351:m 2347:E 2341:l 2331:j 2323:) 2318:l 2315:j 2304:m 2300:i 2286:m 2282:j 2272:l 2269:i 2261:( 2258:= 2246:m 2242:E 2236:l 2226:j 2216:m 2213:l 2210:k 2200:k 2197:j 2194:i 2186:= 2177:i 2173:) 2168:E 2152:( 2117:) 2110:t 2099:d 2096:a 2093:r 2087:E 2074:0 2064:0 2056:+ 2052:J 2046:0 2037:( 2030:t 2015:= 2005:d 2002:a 1999:r 1993:E 1972:) 1966:d 1963:a 1960:r 1954:B 1943:( 1937:t 1922:= 1912:d 1909:a 1906:r 1900:E 1859:d 1856:a 1853:r 1847:E 1821:c 1816:/ 1809:= 1806:k 1786:, 1783:] 1780:) 1777:t 1768:z 1765:k 1762:( 1759:i 1756:[ 1744:c 1741:a 1738:v 1732:E 1727:= 1724:) 1721:t 1718:, 1715:z 1712:( 1706:c 1703:a 1700:v 1694:E 1662:t 1655:/ 1648:c 1645:a 1642:v 1636:E 1626:0 1616:0 1608:= 1602:c 1599:a 1596:v 1590:B 1573:t 1566:/ 1559:c 1556:a 1553:v 1547:B 1536:= 1530:c 1527:a 1524:v 1518:E 1501:0 1498:= 1492:c 1489:a 1486:v 1480:B 1463:0 1460:= 1454:c 1451:a 1448:v 1442:E 1406:) 1399:d 1396:a 1393:r 1387:E 1382:+ 1376:c 1373:a 1370:v 1364:E 1358:( 1349:= 1345:J 1323:J 1297:t 1290:/ 1283:d 1280:a 1277:r 1271:E 1261:0 1251:0 1243:+ 1239:J 1233:0 1225:= 1219:d 1216:a 1213:r 1207:B 1190:t 1183:/ 1176:d 1173:a 1170:r 1164:B 1153:= 1147:d 1144:a 1141:r 1135:E 1118:0 1115:= 1109:d 1106:a 1103:r 1097:B 1080:0 1077:= 1071:d 1068:a 1065:r 1059:E 1023:d 1020:a 1017:r 1011:B 1006:+ 1000:c 997:a 994:v 988:B 983:= 979:B 974:, 968:d 965:a 962:r 956:E 951:+ 945:c 942:a 939:v 933:E 928:= 924:E 896:t 887:E 875:0 863:0 855:+ 851:J 845:0 835:= 827:B 810:t 801:B 788:= 780:E 766:0 763:= 755:B 741:0 738:= 730:E 698:) 695:t 692:, 689:z 686:( 681:R 676:E 668:) 665:t 662:, 659:z 656:( 650:c 647:a 644:v 638:E 630:= 627:) 624:t 621:, 618:z 615:( 609:d 606:a 603:r 597:E 573:R 568:E 543:) 540:t 537:, 534:z 531:( 526:T 521:E 516:+ 513:) 510:t 507:, 504:z 501:( 495:c 492:a 489:v 483:E 475:= 472:) 469:t 466:, 463:z 460:( 454:d 451:a 448:r 442:E 414:T 408:E 383:c 380:a 377:v 371:E 347:. 344:) 341:t 338:, 335:z 332:( 326:d 323:a 320:r 314:E 309:+ 306:) 303:t 300:, 297:z 294:( 288:c 285:a 282:v 276:E 271:= 268:) 265:t 262:, 259:z 256:( 252:E 229:. 226:) 223:t 220:, 217:z 214:( 208:d 205:a 202:r 196:E 171:c 168:a 165:v 159:E

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Knowledge

Ewald–Oseen extinction theorem

Index