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5457:'s double slit interferometer in 1803 demonstrated interference fringes when two small holes were illuminated by light from another small hole which was illuminated by sunlight. Young was able to estimate the wavelength of different colours in the spectrum from the spacing of the fringes. The experiment played a major role in the general acceptance of the wave theory of light. In quantum mechanics, this experiment is considered to demonstrate the inseparability of the wave and particle natures of light and other quantum particles (
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5578:. This technique works by superposing (interfering) the signal waves from the different telescopes on the principle that waves that coincide with the same phase will add to each other while two waves that have opposite phases will cancel each other out. This creates a combined telescope that is equivalent in resolution (though not in sensitivity) to a single antenna whose diameter is equal to the spacing of the antennas farthest apart in the array.
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period will give rise to an interference pattern while they overlap. Two identical waves which consist of a narrow spectrum of frequency waves of finite duration (but shorter than their coherence time), will give a series of fringe patterns of slightly differing spacings, and provided the spread of spacings is significantly less than the average fringe spacing, a fringe pattern will again be observed during the time when the two waves overlap.
270:
amplitudes—this is known as destructive interference. In ideal mediums (water, air are almost ideal) energy is always conserved, at points of destructive interference, the wave amplitudes cancel each other out, and the energy is redistributed to other areas. For example, when two pebbles are dropped in a pond, a pattern is observable; but eventually waves continue, and only when they reach the shore is the energy absorbed away from the medium.
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the wavelength decreases and the summed intensity will show three to four fringes of varying colour. Young describes this very elegantly in his discussion of two slit interference. Since white light fringes are obtained only when the two waves have travelled equal distances from the light source, they can be very useful in interferometry, as they allow the zero path difference fringe to be identified.
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the sum of the displacements of the individual waves. At some points, these will be in phase, and will produce a maximum displacement. In other places, the waves will be in anti-phase, and there will be no net displacement at these points. Thus, parts of the surface will be stationary—these are seen in the figure above and to the right as stationary blue-green lines radiating from the centre.
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Conventional light sources emit waves of differing frequencies and at different times from different points in the source. If the light is split into two waves and then re-combined, each individual light wave may generate an interference pattern with its other half, but the individual fringe patterns
5422:
as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception, the
3188:
It is also possible to observe interference fringes using white light. A white light fringe pattern can be considered to be made up of a 'spectrum' of fringe patterns each of slightly different spacing. If all the fringe patterns are in phase in the centre, then the fringes will increase in size as
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have emission lines with quite narrow frequency spectra. When these are spatially and colour filtered, and then split into two waves, they can be superimposed to generate interference fringes. All interferometry prior to the invention of the laser was done using such sources and had a wide range of
305:
Consider, for example, what happens when two identical stones are dropped into a still pool of water at different locations. Each stone generates a circular wave propagating outwards from the point where the stone was dropped. When the two waves overlap, the net displacement at a particular point is
3150:
Quantum mechanically the theories of Paul Dirac and
Richard Feynman offer a more modern approach. Dirac showed that every quanta or photon of light acts on its own which he famously stated as "every photon interferes with itself". Richard Feynman showed that by evaluating a path integral where all
3159:
The discussion above assumes that the waves which interfere with one another are monochromatic, i.e. have a single frequency—this requires that they are infinite in time. This is not, however, either practical or necessary. Two identical waves of finite duration whose frequency is fixed over that
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on a reflective surface. Light rays from a monochromatic source pass through the glass and reflect off both the bottom surface of the flat and the supporting surface. The tiny gap between the surfaces means the two reflected rays have different path lengths. In addition the ray reflected from the
5499:
system was defined to be equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum. This definition was replaced in 1983 by defining the metre as the distance travelled by light in vacuum during a specific time interval.
3184:
Normally, a single laser beam is used in interferometry, though interference has been observed using two independent lasers whose frequencies were sufficiently matched to satisfy the phase requirements. This has also been observed for widefield interference between two incoherent laser sources.
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generally approximates much more closely to a monochromatic source, and thus it is much more straightforward to generate interference fringes using a laser. The ease with which interference fringes can be observed with a laser beam can sometimes cause problems in that stray reflections may give
269:
of a wave meets a crest of another wave of the same frequency at the same point, then the amplitude is the sum of the individual amplitudes—this is constructive interference. If a crest of one wave meets a trough of another wave, then the amplitude is equal to the difference in the individual
309:
Interference of light is a unique phenomenon in that we can never observe superposition of the EM field directly as we can, for example, in water. Superposition in the EM field is an assumed phenomenon and necessary to explain how two light beams pass through each other and continue on their
1783:
produces a spherical wave. If the light from two point sources overlaps, the interference pattern maps out the way in which the phase difference between the two waves varies in space. This depends on the wavelength and on the separation of the point sources. The figure to the right shows
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was developed. Astronomical radio interferometers usually consist either of arrays of parabolic dishes or two-dimensional arrays of omni-directional antennas. All of the telescopes in the array are widely separated and are usually connected together using
3235:. For example, the colours seen in a soap bubble arise from interference of light reflecting off the front and back surfaces of the thin soap film. Depending on the thickness of the film, different colours interfere constructively and destructively.
3142:
to give rise to interference fringes since it is not possible for waves of different polarizations to cancel one another out or add together. Instead, when waves of different polarization are added together, they give rise to a wave of a different
3151:
possible paths are considered, that a number of higher probability paths will emerge. In thin films for example, film thickness which is not a multiple of light wavelength will not allow the quanta to traverse, only reflection is possible.
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of an optical interference pattern. The intensity of the light at a given point is proportional to the square of the average amplitude of the wave. This can be expressed mathematically as follows. The displacement of the two waves at a point
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To generate interference fringes, light from the source has to be divided into two waves which then have to be re-combined. Traditionally, interferometers have been classified as either amplitude-division or wavefront-division systems.
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Photograph of 1.5cm x 1cm region of soap film under white light. Varying film thickness and viewing geometry determine which colours undergo constructive or destructive interference. Small bubbles significantly affect surrounding film
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Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. Thus, an interference fringe pattern is produced, where the separation of the maxima is
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of the same frequency intersect at an angle. One wave is travelling horizontally, and the other is travelling downwards at an angle θ to the first wave. Assuming that the two waves are in phase at the point
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Real wave interference is obtained simply by adding the displacements from equilibrium (or amplitudes) of the two waves; In complex wave interference, we measure the modulus of the wavefunction squared.
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where the path difference is an even multiple of λ/2 the waves cancel. Since the gap between the surfaces varies slightly in width at different points, a series of alternating bright and dark bands,
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can be considered to be a multiple-beam interferometer; since the peaks which it produces are generated by interference between the light transmitted by each of the elements in the grating; see
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Because the frequency of light waves (~10 Hz) is too high for currently available detectors to detect the variation of the electric field of the light, it is possible to observe only the
302:. If the difference between the phases is intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values.
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5799:. Leika Science Lab, 09 June 2011. "If two waves interfere, the amplitude of the resulting light wave will be equal to the vector sum of the amplitudes of the two interfering waves."
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It is sometimes desirable for several waves of the same frequency and amplitude to sum to zero (that is, interfere destructively, cancel). This is the principle behind, for example,
1615:
2927:{\displaystyle I(\mathbf {r} )=\int U(\mathbf {r} ,t)U^{*}(\mathbf {r} ,t)\,dt\propto A_{1}^{2}(\mathbf {r} )+A_{2}^{2}(\mathbf {r} )+2A_{1}(\mathbf {r} )A_{2}(\mathbf {r} )\cos.}
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will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a
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creates ultrasonic waves that are radiated into the medium. The waves strike a reflector placed parallel to the crystal, reflected back to the source and measured.
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Interferometry has played an important role in the advancement of physics, and also has a wide range of applications in physical and engineering measurement.
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generated will have different phases and spacings, and normally no overall fringe pattern will be observable. However, single-element light sources, such as
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When the plane of observation is far enough away, the fringe pattern will be a series of almost straight lines, since the waves will then be almost planar.
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interference between two spherical waves. The wavelength increases from top to bottom, and the distance between the sources increases from left to right.
3131:
Thus, the interference pattern maps out the difference in phase between the two waves, with maxima occurring when the phase difference is a multiple of 2
4935:
indicates that the object can be in situation A or situation B. The above equation can then be interpreted as: The probability of finding the object at
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Interference occurs when several waves are added together provided that the phase differences between them remain constant over the observation time.
1934:
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is used to divide the light into two beams travelling in different directions, which are then superimposed to produce the interference pattern. The
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4751:{\displaystyle P(x)=|\Psi (x,t)|^{2}=|\Psi _{A}(x,t)|^{2}+|\Psi _{B}(x,t)|^{2}+(\Psi _{A}^{*}(x,t)\Psi _{B}(x,t)+\Psi _{A}(x,t)\Psi _{B}^{*}(x,t))}
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This represents a wave at the original frequency, traveling to the right like its components, whose amplitude is proportional to the cosine of
6362:
5574:. Interferometry increases the total signal collected, but its primary purpose is to vastly increase the resolution through a process called
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was fond of saying that all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment.
3135:. If the two beams are of equal intensity, the maxima are four times as bright as the individual beams, and the minima have zero intensity.
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2003:
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160:) if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example,
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line in the new standard, and also showed that it could be used as a length standard. Sixty years later, in 1960, the metre in the new
1809:
It is easy to see that a set of waves will cancel if they have the same amplitude and their phases are spaced equally in angle. Using
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The above can be demonstrated in one dimension by deriving the formula for the sum of two waves. The equation for the amplitude of a
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of the wave. Suppose a second wave of the same frequency and amplitude but with a different phase is also traveling to the right
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in the above equation depending on whether the quantum interference term is positive or negative. If this term is absent for all
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42:
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5725:. University College London (UCL) UCL Library Services. London : printed by W. Bulmer and Co., Cleveland Row, St. James's.
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Interference of right traveling (green) and left traveling (blue) waves in Two-dimensional space, resulting in final (red) wave
4847:
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3122:{\displaystyle I(\mathbf {r} )=I_{1}(\mathbf {r} )+I_{2}(\mathbf {r} )+2{\sqrt {I_{1}(\mathbf {r} )I_{2}(\mathbf {r} )}}\cos.}
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function. A classical wave at any point can be positive or negative; the quantum probability function is non-negative.
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above, the quantum interference term can add (constructive interference) or subtract (destructive interference) from
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90:
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On the mechanism of the eye / by Thomas Young.; Young, Thomas; University
College, London Library Services (1801).
5352:. The interference pattern occurs on the far side, observed by detectors suitable to the particles originating the
3483:
1370:
972:{\displaystyle W_{1}+W_{2}=2A\cos \left({\varphi \over 2}\right)\cos \left(kx-\omega t+{\varphi \over 2}\right).}
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5431:, as the beat frequency of any two tones is equivalent to the frequency of their implied fundamental frequency.
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states that when two or more propagating waves of the same type are incident on the same point, the resultant
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4384:. Quantum interference concerns the issue of this probability when the wavefunction is expressed as a sum or
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function representing the displacement from an equilibrium position; an optical or quantum wavefunction is a
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Optical interference between two point sources that have different wavelengths and separations of sources.
1323:
119:: (here by 180 degrees), the two lower waves combine (right panel), resulting in a wave of zero amplitude
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to interfere. In practice this means the wave must come from the same source and have similar frequencies
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Cropped tomography scan animation of laser light interference passing through two pinholes (side edges).
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The fringes are observed wherever the two waves overlap and the fringe spacing is uniform throughout.
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instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a
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1526:{\displaystyle \Delta \varphi ={\frac {2\pi d}{\lambda }}={\frac {2\pi x\sin \theta }{\lambda }}.}
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1681:{\displaystyle {\frac {x\sin \theta }{\lambda }}=\pm {\frac {1}{2}},\pm {\frac {3}{2}},\ldots }
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from electrons, atoms or molecules approach a barrier with two slits in it. One slit becomes
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The
Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory
2164:. Some of the differences between real valued and complex valued wave interference include:
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5487:. When the metre was defined as the distance between two marks on a platinum-iridium bar,
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The interference involves different types of mathematical functions: A classical wave is a
1902:
852:{\textstyle \cos a+\cos b=2\cos \left({a-b \over 2}\right)\cos \left({a+b \over 2}\right),}
142:
are combined by adding their intensities or displacements with due consideration for their
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where the path difference is an odd multiple of λ/2, the waves reinforce. At locations
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5257:, then there is no quantum mechanical interference associated with situations A and B.
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2660:{\displaystyle U(\mathbf {r} ,t)=A_{1}(\mathbf {r} )e^{i}+A_{2}(\mathbf {r} )e^{i}.}
1806:. In both of these cases, the result is achieved by uniform spacing of the phases.
329:
In addition to classical wave model for understanding optical interference, quantum
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when it is in situation B plus an extra term. This extra term, which is called the
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111:: the two lower waves combine (left panel), resulting in a wave of added amplitude
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which means "hit or strike", and was used in the context of wave superposition by
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are generally considered to be the first strong evidence against the theory of a
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5122:{\displaystyle \Psi _{A}^{*}(x,t)\Psi _{B}(x,t)+\Psi _{A}(x,t)\Psi _{B}^{*}(x,t)}
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Any two different real waves in the same medium interfere; complex waves must be
2145:
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Pfleegor, R. L.; Mandel, L. (1967). "Interference of independent photon beams".
5590:
is an instrument for measuring the physical characteristics of sound waves in a
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correspond to distinct situations A and B. When this is the case, the equation
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is known as the fringe spacing. The fringe spacing increases with increase in
323:
5772:
1313:{\displaystyle \varphi =\ldots ,-3\pi ,\,-\pi ,\,\pi ,\,3\pi ,\,5\pi ,\ldots }
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3376:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }
3202:
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This can be expressed in terms of the intensities of the individual waves as
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Bach, Roger; Pope, Damian; Liou, Sy-Hwang; Batelaan, Herman (2013-03-13).
294:(180°), whereas destructive interference occurs when the difference is an
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In wavefront-division systems, the wave is divided in space—examples are
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bottom plate undergoes a 180° phase reversal. As a result, at locations
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when it is in situation A plus the probability of finding the object at
1601:{\displaystyle {\frac {x\sin \theta }{\lambda }}=0,\pm 1,\pm 2,\ldots ,}
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respective paths. Prime examples of light interference are the famous
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Easy JavaScript
Simulation Model of One Dimensional Wave Interference
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and Benoît used interferometry to measure the wavelength of the red
1091:{\displaystyle \varphi =\ldots ,-4\pi ,-2\pi ,0,2\pi ,4\pi ,\ldots }
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108:
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220:
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1154:, so the sum of the two waves is a wave with twice the amplitude
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is produced. This combination tone can also be referred to as a
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can be directly observed: they are real-valued wave functions;
2075:
one merely assumes the converse, then multiplies both sides by
1991:{\displaystyle \varphi _{n}-\varphi _{n-1}={\frac {2\pi }{N}}.}
1810:
619:
37:"Interference pattern" redirects here. For Moiré patterns, see
4373:{\displaystyle P(x)=|\Psi (x,t)|^{2}=\Psi ^{*}(x,t)\Psi (x,t)}
2457:{\displaystyle U_{2}(\mathbf {r} ,t)=A_{2}(\mathbf {r} )e^{i}}
2344:{\displaystyle U_{1}(\mathbf {r} ,t)=A_{1}(\mathbf {r} )e^{i}}
6034:
This is Your Brain on Music: The
Science of a Human Obsession
5388:
197:
3227:
Interference can also be seen in everyday phenomena such as
1771:
5869:
Patel, R.; Achamfuo-Yeboah, S.; Light R.; Clark M. (2014).
139:
3181:
spurious interference fringes which can result in errors.
5591:
5483:
Interferometry has been used in defining and calibrating
5230:{\displaystyle |\Psi _{A}(x,t)|^{2}+|\Psi _{B}(x,t)|^{2}}
1437:
A simple form of interference pattern is obtained if two
5515:. It is also used in the testing of optical components.
5500:
Interferometry is still fundamental in establishing the
4928:{\displaystyle \Psi (x,t)=\Psi _{A}(x,t)+\Psi _{B}(x,t)}
4472:{\displaystyle \Psi (x,t)=\Psi _{A}(x,t)+\Psi _{B}(x,t)}
27:
Phenomenon resulting from the superposition of two waves
5496:
5356:. The pattern matches the optical double slit pattern.
1425:
Geometrical arrangement for two plane wave interference
5260:
The best known example of quantum interference is the
1734:{\displaystyle d_{f}={\frac {\lambda }{\sin \theta }}}
754:
591:{\displaystyle W_{2}(x,t)=A\cos(kx-\omega t+\varphi )}
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cannot be directly observed: they are complex valued
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2066:{\displaystyle \sum _{n=0}^{N-1}Ae^{i\varphi _{n}}=0}
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1326:
1245:
1160:
1104:
1024:
985:
865:
632:
604:
523:
487:
446:
426:
351:
5974:
1535:
It can be seen that the two waves are in phase when
63:
may be too technical for most readers to understand
5344:
5302:
5249:
5229:
5121:
4987:
4967:
4947:
4927:
4836:
4794:
4750:
4471:
4372:
4259:
4239:
4199:
3375:
3121:
2926:
2659:
2456:
2343:
2112:
2065:
1990:
1923:
1891:
1865:
1845:
1733:
1680:
1600:
1525:
1405:
1359:
1312:
1222:
1146:
1090:
999:
971:
851:
736:
610:
590:
505:
469:
432:
412:
5764:History of the Principle of Interference of Light
1014:: If the phase difference is an even multiple of
148:. The resultant wave may have greater intensity (
6933:
6123:Java simulation of interference of water waves 2
6118:Java simulation of interference of water waves 1
5742:. Oxford Music Online. Oxford University Press.
2140:
2126:uses interference between multiple reflections.
1235:: If the phase difference is an odd multiple of
345:wave traveling to the right along the x-axis is
265:of the amplitudes of the individual waves. If a
184:as well as in loudspeakers as electrical waves.
5961:, The Feynman Lectures Website, September 2013.
5916:
5914:
1433:Interference fringes in overlapping plane waves
1223:{\displaystyle W_{1}+W_{2}=2A\cos(kx-\omega t)}
1147:{\displaystyle \left|\cos(\varphi /2)\right|=1}
5833:
2470:represents the magnitude of the displacement,
1766:
30:For interference in radio communications, see
6155:
5977:"Controlled double-slit electron diffraction"
5963:"The Feynman Lectures on Physics, Volume III"
5507:Interferometry is used in the calibration of
4142:
3138:Classically the two waves must have the same
618:is the phase difference between the waves in
413:{\displaystyle W_{1}(x,t)=A\cos(kx-\omega t)}
336:
232:Interference of waves from two point sources.
5911:
4955:is the probability of finding the object at
3370:
3344:
3239:Iridiscence caused by thin-film interference
3213:are examples of amplitude-division systems.
3154:
2190:
1446:, then the relative phase changes along the
6128:Flash animations demonstrating interference
6050:
5423:beating starts to sound like a note, and a
6162:
6148:
6113:Expressions of position and fringe spacing
5581:
4215:for a quantum mechanical object. Then the
4149:
4135:
3274:White light interference in a soap bubble.
1416:
282:Constructive interference occurs when the
5992:
5930:. Cambridge: Cambridge University Press.
5894:
5813:. Cambridge: Cambridge University Press.
5440:
4169:
2751:
1450:-axis. The phase difference at the point
1356:
1297:
1287:
1280:
1270:
91:Learn how and when to remove this message
75:, without removing the technical details.
5920:
5528:
2485:The displacement of the summed waves is
2194:
2113:{\displaystyle e^{i{\frac {2\pi }{N}}}.}
1770:
1428:
1420:
272:
235:
227:
219:
102:
6031:
5748:10.1093/gmo/9781561592630.article.20622
5518:
5511:(called gauge blocks in the US) and in
3279:
3192:
2199:Creation of interference fringes by an
1610:and are half a cycle out of phase when
43:Interference pattern (electromyography)
14:
6934:
6056:
5760:
1367:, so the sum of the two waves is zero
6169:
6143:
5808:
5735:
3250:Smartphone with iridescent back panel
626:and add: the sum of the two waves is
73:make it understandable to non-experts
5871:"Widefield two laser interferometry"
4247:of observing the object at position
1360:{\displaystyle \cos(\varphi /2)=0\,}
47:
3201:In an amplitude-division system, a
286:difference between the waves is an
255:principle of superposition of waves
24:
6066:. New York: W.W. Norton. pp.
5318:
5276:
5191:
5146:
5090:
5065:
5037:
5007:
4901:
4873:
4851:
4810:
4768:
4716:
4691:
4663:
4633:
4590:
4545:
4506:
4445:
4417:
4395:
4352:
4328:
4294:
4179:
3681:Sum-over-histories (path integral)
3367:
3341:
3297:Part of a series of articles about
3218:Young's double slit interferometer
1846:{\displaystyle Ae^{i\varphi _{n}}}
1813:, each wave can be represented as
1463:
25:
6958:
6101:
5129:in the above equation. As in the
3318:
1790:
6916:
6915:
3267:
3255:
3243:
3106:
3082:
3050:
3029:
3000:
2976:
2952:
2911:
2887:
2857:
2836:
2809:
2780:
2738:
2711:
2691:
2633:
2601:
2563:
2531:
2501:
2433:
2401:
2371:
2320:
2288:
2258:
470:{\displaystyle k=2\pi /\lambda }
333:also demonstrate interference.
52:
6092:Geometrical and Physical Optics
6084:
6025:
5359:
5130:
107:The interference of two waves.
6865:Relativistic quantum mechanics
5944:
5862:
5827:
5802:
5789:
5754:
5729:
5712:
5345:{\displaystyle \Psi _{B}(x,t)}
5339:
5327:
5303:{\displaystyle \Psi _{A}(x,t)}
5297:
5285:
5217:
5212:
5200:
5186:
5172:
5167:
5155:
5141:
5116:
5104:
5086:
5074:
5058:
5046:
5033:
5021:
4922:
4910:
4894:
4882:
4866:
4854:
4837:{\displaystyle \Psi _{B}(x,t)}
4831:
4819:
4795:{\displaystyle \Psi _{A}(x,t)}
4789:
4777:
4745:
4742:
4730:
4712:
4700:
4684:
4672:
4659:
4647:
4629:
4616:
4611:
4599:
4585:
4571:
4566:
4554:
4540:
4526:
4521:
4509:
4502:
4495:
4489:
4466:
4454:
4438:
4426:
4410:
4398:
4367:
4355:
4349:
4337:
4314:
4309:
4297:
4290:
4283:
4277:
4234:
4228:
4194:
4182:
3831:Relativistic quantum mechanics
3363:
3356:
3337:
3113:
3110:
3102:
3086:
3078:
3065:
3054:
3046:
3033:
3025:
3004:
2996:
2980:
2972:
2956:
2948:
2918:
2915:
2907:
2891:
2883:
2870:
2861:
2853:
2840:
2832:
2813:
2805:
2784:
2776:
2748:
2734:
2721:
2707:
2695:
2687:
2669:The intensity of the light at
2649:
2637:
2629:
2616:
2605:
2597:
2579:
2567:
2559:
2546:
2535:
2527:
2511:
2497:
2449:
2437:
2429:
2416:
2405:
2397:
2381:
2367:
2336:
2324:
2316:
2303:
2292:
2284:
2268:
2254:
1347:
1333:
1217:
1199:
1130:
1116:
737:{\displaystyle W_{1}+W_{2}=A.}
728:
725:
701:
689:
671:
662:
585:
561:
546:
534:
506:{\displaystyle \omega =2\pi f}
407:
389:
374:
362:
261:at that point is equal to the
13:
1:
6843:Quantum statistical mechanics
6620:Quantum differential calculus
6542:Delayed-choice quantum eraser
6325:Symmetry in quantum mechanics
6003:10.1088/1367-2630/15/3/033018
5987:(3). IOP Publishing: 033018.
5705:
5513:coordinate-measuring machines
5504:chain in length measurement.
3871:Quantum statistical mechanics
2141:Complex valued wave functions
1406:{\displaystyle W_{1}+W_{2}=0}
215:
135:is a phenomenon in which two
5694:Rayleigh roughness criterion
5553:In 1946, a technique called
2135:interference vs. diffraction
1756:, and with decreasing angle
748:for the sum of two cosines:
187:
41:. For the medical term, see
32:Interference (communication)
7:
6645:Quantum stochastic calculus
6635:Quantum measurement problem
6557:Mach–Zehnder interferometer
6032:Levitin, Daniel J. (2006).
5616:
5555:astronomical interferometry
5525:Astronomical interferometer
5470:Michelson–Morley experiment
5399:as a periodic variation in
3841:Quantum information science
3211:Mach–Zehnder interferometer
1767:Between two spherical waves
113:(constructive interference)
10:
6963:
5736:Jones, Peter Ward (2001).
5522:
5444:
5433:
5368:
4200:{\displaystyle \Psi (x,t)}
3283:
2124:Fabry–Pérot interferometer
1000:{\displaystyle \varphi /2}
337:Real-valued wave functions
204:which means "between" and
121:(destructive interference)
36:
29:
6911:
6873:
6825:
6705:Quantum complexity theory
6683:Quantum cellular automata
6658:
6590:
6524:
6437:
6401:
6388:Path integral formulation
6355:
6220:
6177:
6094:, 1968, Longmans, London.
5773:10.1007/978-3-0348-8652-9
5541:formed from many smaller
4997:quantum interference term
3173:successful applications.
3155:Light source requirements
2474:represents the phase and
2191:Optical wave interference
1012:Constructive interference
151:constructive interference
6772:Quantum machine learning
6752:Quantum key distribution
6742:Quantum image processing
6732:Quantum error correction
6582:Wheeler's delayed choice
5856:10.1103/physrev.159.1084
5722:Young, Thomas, 1773-1829
5649:Interference lithography
5407:of the two frequencies.
3876:Quantum machine learning
3629:Wheeler's delayed-choice
3207:Michelson interferometer
2137:for further discussion.
1233:Destructive interference
611:{\displaystyle \varphi }
320:anti-reflective coatings
157:destructive interference
18:Destructive interference
6688:Quantum finite automata
5739:Oxford University Press
5654:Interference visibility
5588:acoustic interferometer
5582:Acoustic interferometry
5364:
5310:and the other becomes
4166:wave-behavior of matter
3586:Leggett–Garg inequality
1417:Between two plane waves
440:is the peak amplitude,
6792:Quantum neural network
6036:. Dutton. p. 22.
5981:New Journal of Physics
5761:Kipnis, Nahum (1991).
5689:Thin-film interference
5674:Multipath interference
5550:
5447:Optical interferometry
5441:Optical interferometry
5391:of slightly different
5346:
5304:
5264:. In this experiment,
5262:double-slit experiment
5251:
5231:
5123:
4989:
4969:
4949:
4929:
4838:
4796:
4752:
4473:
4374:
4261:
4241:
4201:
3377:
3286:Double-slit experiment
3123:
2928:
2661:
2458:
2345:
2221:
2166:
2114:
2067:
2033:
1992:
1925:
1893:
1867:
1847:
1776:
1735:
1682:
1602:
1527:
1434:
1426:
1407:
1361:
1314:
1224:
1148:
1092:
1001:
973:
853:
746:trigonometric identity
738:
622:. The two waves will
612:
592:
507:
471:
434:
414:
312:double-slit experiment
279:
250:
233:
225:
154:) or lower amplitude (
124:
6817:Quantum teleportation
6345:Wave–particle duality
5924:; Wolf, Emil (1999).
5809:Steel, W. H. (1986).
5539:interferometric array
5532:
5459:wave–particle duality
5347:
5305:
5252:
5232:
5124:
4990:
4970:
4950:
4930:
4839:
4797:
4753:
4474:
4375:
4262:
4242:
4202:
3571:Elitzur–Vaidman
3561:Davisson–Germer
3378:
3233:structural coloration
3124:
2929:
2662:
2459:
2346:
2198:
2115:
2068:
2007:
1993:
1926:
1924:{\displaystyle n=N-1}
1894:
1868:
1848:
1774:
1736:
1683:
1603:
1528:
1432:
1424:
1408:
1362:
1315:
1225:
1149:
1093:
1002:
974:
854:
739:
613:
593:
508:
472:
435:
415:
276:
248:
231:
223:
106:
6848:Quantum field theory
6777:Quantum metamaterial
6722:Quantum cryptography
6452:Consistent histories
5927:Principles of Optics
5896:10.1364/OE.22.027094
5624:Active noise control
5519:Radio interferometry
5387:pattern between two
5314:
5272:
5241:
5137:
5003:
4979:
4959:
4939:
4848:
4806:
4764:
4483:
4392:
4386:linear superposition
4271:
4251:
4240:{\displaystyle P(x)}
4222:
4213:Schrödinger equation
4176:
4170:optical interference
4162:Quantum interference
3836:Quantum field theory
3748:Consistent histories
3385:Schrödinger equation
3312:
3280:Quantum interference
3193:Optical arrangements
2942:
2681:
2491:
2354:
2241:
2218:interference fringes
2079:
2004:
1935:
1903:
1877:
1857:
1817:
1697:
1616:
1541:
1460:
1371:
1324:
1243:
1158:
1102:
1022:
983:
863:
859:this can be written
752:
630:
602:
521:
485:
444:
424:
349:
196:is derived from the
6833:Quantum fluctuation
6802:Quantum programming
6762:Quantum logic gates
6747:Quantum information
6727:Quantum electronics
6202:Classical mechanics
5887:2014OExpr..2227094P
5881:(22): 27094–27101.
5848:1967PhRv..159.1084P
5684:Optical path length
5634:Coherence (physics)
5570:, or other type of
5545:, like many larger
5474:luminiferous aether
5468:The results of the
5429:missing fundamental
5131:classical wave case
5103:
5020:
4729:
4646:
4382:complex conjugation
3624:Stern–Gerlach
3421:Classical mechanics
3170:mercury-vapor lamps
2804:
2775:
2131:diffraction grating
1892:{\displaystyle n=0}
1804:diffraction grating
174:surface water waves
6886:in popular culture
6668:Quantum algorithms
6516:Von Neumann–Wigner
6496:Objective collapse
6207:Old quantum theory
6133:2009-06-24 at the
5576:Aperture synthesis
5551:
5478:special relativity
5403:whose rate is the
5342:
5300:
5247:
5227:
5119:
5089:
5006:
4985:
4965:
4945:
4925:
4834:
4792:
4748:
4715:
4632:
4469:
4380:where * indicates
4370:
4257:
4237:
4197:
3812:Von Neumann–Wigner
3792:Objective-collapse
3591:Mach–Zehnder
3581:Leggett inequality
3576:Franck–Hertz
3426:Old quantum theory
3373:
3145:polarization state
3119:
2924:
2790:
2761:
2657:
2454:
2341:
2222:
2110:
2063:
1988:
1921:
1889:
1863:
1843:
1777:
1731:
1678:
1598:
1523:
1435:
1427:
1403:
1357:
1310:
1220:
1144:
1088:
997:
969:
849:
734:
608:
588:
503:
467:
430:
410:
280:
251:
234:
226:
125:
6929:
6928:
6903:Quantum mysticism
6881:Schrödinger's cat
6812:Quantum simulator
6782:Quantum metrology
6710:Quantum computing
6673:Quantum amplifier
6650:Quantum spacetime
6615:Quantum cosmology
6605:Quantum chemistry
6320:Scattering theory
6268:Zero-point energy
6263:Degenerate levels
6171:Quantum mechanics
6077:978-0-393-04688-5
5782:978-3-0348-9717-4
5644:Haidinger fringes
5572:transmission line
5250:{\displaystyle x}
4988:{\displaystyle x}
4968:{\displaystyle x}
4948:{\displaystyle x}
4260:{\displaystyle x}
4159:
4158:
3866:Scattering theory
3846:Quantum computing
3619:Schrödinger's cat
3551:Bell's inequality
3359:
3334:
3303:Quantum mechanics
3057:
2480:angular frequency
2103:
1983:
1866:{\displaystyle N}
1729:
1670:
1654:
1638:
1563:
1518:
1488:
959:
916:
840:
808:
515:angular frequency
433:{\displaystyle A}
246:
101:
100:
93:
16:(Redirected from
6954:
6919:
6918:
6630:Quantum geometry
6625:Quantum dynamics
6482:Superdeterminism
6378:Matrix mechanics
6233:Bra–ket notation
6164:
6157:
6150:
6141:
6140:
6095:
6088:
6082:
6081:
6054:
6048:
6047:
6029:
6023:
6022:
5996:
5972:
5966:
5965:(online edition)
5948:
5942:
5941:
5918:
5909:
5908:
5898:
5866:
5860:
5859:
5842:(5): 1084–1088.
5831:
5825:
5824:
5806:
5800:
5795:Ockenga, Wymke.
5793:
5787:
5786:
5758:
5752:
5751:
5733:
5727:
5726:
5716:
5629:Beat (acoustics)
5594:or liquid, such
5547:radio telescopes
5535:Very Large Array
5485:length standards
5476:and in favor of
5425:combination tone
5371:Beat (acoustics)
5351:
5349:
5348:
5343:
5326:
5325:
5309:
5307:
5306:
5301:
5284:
5283:
5256:
5254:
5253:
5248:
5236:
5234:
5233:
5228:
5226:
5225:
5220:
5199:
5198:
5189:
5181:
5180:
5175:
5154:
5153:
5144:
5128:
5126:
5125:
5120:
5102:
5097:
5073:
5072:
5045:
5044:
5019:
5014:
4994:
4992:
4991:
4986:
4974:
4972:
4971:
4966:
4954:
4952:
4951:
4946:
4934:
4932:
4931:
4926:
4909:
4908:
4881:
4880:
4843:
4841:
4840:
4835:
4818:
4817:
4801:
4799:
4798:
4793:
4776:
4775:
4757:
4755:
4754:
4749:
4728:
4723:
4699:
4698:
4671:
4670:
4645:
4640:
4625:
4624:
4619:
4598:
4597:
4588:
4580:
4579:
4574:
4553:
4552:
4543:
4535:
4534:
4529:
4505:
4478:
4476:
4475:
4470:
4453:
4452:
4425:
4424:
4379:
4377:
4376:
4371:
4336:
4335:
4323:
4322:
4317:
4293:
4266:
4264:
4263:
4258:
4246:
4244:
4243:
4238:
4211:solution of the
4206:
4204:
4203:
4198:
4151:
4144:
4137:
3778:Superdeterminism
3431:Bra–ket notation
3382:
3380:
3379:
3374:
3366:
3361:
3360:
3352:
3340:
3335:
3333:
3322:
3294:
3293:
3271:
3259:
3247:
3134:
3128:
3126:
3125:
3120:
3109:
3101:
3100:
3085:
3077:
3076:
3058:
3053:
3045:
3044:
3032:
3024:
3023:
3014:
3003:
2995:
2994:
2979:
2971:
2970:
2955:
2933:
2931:
2930:
2925:
2914:
2906:
2905:
2890:
2882:
2881:
2860:
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2851:
2839:
2831:
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2812:
2803:
2798:
2783:
2774:
2769:
2741:
2733:
2732:
2714:
2694:
2674:
2666:
2664:
2663:
2658:
2653:
2652:
2636:
2628:
2627:
2604:
2596:
2595:
2583:
2582:
2566:
2558:
2557:
2534:
2526:
2525:
2504:
2477:
2473:
2469:
2463:
2461:
2460:
2455:
2453:
2452:
2436:
2428:
2427:
2404:
2396:
2395:
2374:
2366:
2365:
2350:
2348:
2347:
2342:
2340:
2339:
2323:
2315:
2314:
2291:
2283:
2282:
2261:
2253:
2252:
2234:
2119:
2117:
2116:
2111:
2106:
2105:
2104:
2099:
2091:
2072:
2070:
2069:
2064:
2056:
2055:
2054:
2053:
2032:
2021:
1997:
1995:
1994:
1989:
1984:
1979:
1971:
1966:
1965:
1947:
1946:
1930:
1928:
1927:
1922:
1898:
1896:
1895:
1890:
1872:
1870:
1869:
1864:
1852:
1850:
1849:
1844:
1842:
1841:
1840:
1839:
1759:
1751:
1740:
1738:
1737:
1732:
1730:
1728:
1714:
1709:
1708:
1687:
1685:
1684:
1679:
1671:
1663:
1655:
1647:
1639:
1634:
1620:
1607:
1605:
1604:
1599:
1564:
1559:
1545:
1532:
1530:
1529:
1524:
1519:
1514:
1494:
1489:
1484:
1473:
1412:
1410:
1409:
1404:
1396:
1395:
1383:
1382:
1366:
1364:
1363:
1358:
1343:
1319:
1317:
1316:
1311:
1238:
1229:
1227:
1226:
1221:
1183:
1182:
1170:
1169:
1153:
1151:
1150:
1145:
1137:
1133:
1126:
1097:
1095:
1094:
1089:
1017:
1006:
1004:
1003:
998:
993:
978:
976:
975:
970:
965:
961:
960:
952:
921:
917:
909:
888:
887:
875:
874:
858:
856:
855:
850:
845:
841:
836:
825:
813:
809:
804:
793:
743:
741:
740:
735:
655:
654:
642:
641:
617:
615:
614:
609:
597:
595:
594:
589:
533:
532:
512:
510:
509:
504:
476:
474:
473:
468:
463:
439:
437:
436:
431:
419:
417:
416:
411:
361:
360:
301:
293:
247:
145:phase difference
96:
89:
85:
82:
76:
56:
55:
48:
21:
6962:
6961:
6957:
6956:
6955:
6953:
6952:
6951:
6932:
6931:
6930:
6925:
6907:
6893:Wigner's friend
6869:
6860:Quantum gravity
6821:
6807:Quantum sensing
6787:Quantum network
6767:Quantum machine
6737:Quantum imaging
6700:Quantum circuit
6695:Quantum channel
6654:
6600:Quantum biology
6586:
6562:Elitzur–Vaidman
6537:Davisson–Germer
6520:
6472:Hidden-variable
6462:de Broglie–Bohm
6439:Interpretations
6433:
6397:
6351:
6238:Complementarity
6216:
6173:
6168:
6135:Wayback Machine
6104:
6099:
6098:
6090:RS Longhurst,
6089:
6085:
6078:
6055:
6051:
6044:
6030:
6026:
5973:
5969:
5949:
5945:
5938:
5919:
5912:
5867:
5863:
5832:
5828:
5821:
5807:
5803:
5794:
5790:
5783:
5759:
5755:
5734:
5730:
5717:
5713:
5708:
5703:
5619:
5613:
5584:
5527:
5521:
5463:Richard Feynman
5449:
5443:
5438:
5373:
5367:
5362:
5321:
5317:
5315:
5312:
5311:
5279:
5275:
5273:
5270:
5269:
5242:
5239:
5238:
5221:
5216:
5215:
5194:
5190:
5185:
5176:
5171:
5170:
5149:
5145:
5140:
5138:
5135:
5134:
5098:
5093:
5068:
5064:
5040:
5036:
5015:
5010:
5004:
5001:
5000:
4980:
4977:
4976:
4960:
4957:
4956:
4940:
4937:
4936:
4904:
4900:
4876:
4872:
4849:
4846:
4845:
4813:
4809:
4807:
4804:
4803:
4771:
4767:
4765:
4762:
4761:
4724:
4719:
4694:
4690:
4666:
4662:
4641:
4636:
4620:
4615:
4614:
4593:
4589:
4584:
4575:
4570:
4569:
4548:
4544:
4539:
4530:
4525:
4524:
4501:
4484:
4481:
4480:
4448:
4444:
4420:
4416:
4393:
4390:
4389:
4331:
4327:
4318:
4313:
4312:
4289:
4272:
4269:
4268:
4252:
4249:
4248:
4223:
4220:
4219:
4177:
4174:
4173:
4164:– the observed
4155:
4126:
4125:
4124:
3889:
3881:
3880:
3826:
3825:Advanced topics
3818:
3817:
3816:
3768:Hidden-variable
3758:de Broglie–Bohm
3737:
3735:Interpretations
3727:
3726:
3725:
3695:
3687:
3686:
3685:
3643:
3635:
3634:
3633:
3600:
3556:CHSH inequality
3545:
3537:
3536:
3535:
3464:Complementarity
3458:
3450:
3449:
3448:
3416:
3387:
3362:
3351:
3350:
3336:
3326:
3321:
3313:
3310:
3309:
3292:
3282:
3275:
3272:
3263:
3260:
3251:
3248:
3195:
3157:
3132:
3105:
3096:
3092:
3081:
3072:
3068:
3049:
3040:
3036:
3028:
3019:
3015:
3013:
2999:
2990:
2986:
2975:
2966:
2962:
2951:
2943:
2940:
2939:
2910:
2901:
2897:
2886:
2877:
2873:
2856:
2847:
2843:
2835:
2826:
2822:
2808:
2799:
2794:
2779:
2770:
2765:
2737:
2728:
2724:
2710:
2690:
2682:
2679:
2678:
2670:
2632:
2623:
2619:
2612:
2608:
2600:
2591:
2587:
2562:
2553:
2549:
2542:
2538:
2530:
2521:
2517:
2500:
2492:
2489:
2488:
2478:represents the
2475:
2471:
2467:
2432:
2423:
2419:
2412:
2408:
2400:
2391:
2387:
2370:
2361:
2357:
2355:
2352:
2351:
2319:
2310:
2306:
2299:
2295:
2287:
2278:
2274:
2257:
2248:
2244:
2242:
2239:
2238:
2230:
2193:
2143:
2092:
2090:
2086:
2082:
2080:
2077:
2076:
2049:
2045:
2041:
2037:
2022:
2011:
2005:
2002:
2001:
1972:
1970:
1955:
1951:
1942:
1938:
1936:
1933:
1932:
1904:
1901:
1900:
1878:
1875:
1874:
1858:
1855:
1854:
1835:
1831:
1827:
1823:
1818:
1815:
1814:
1793:
1769:
1757:
1749:
1744:
1718:
1713:
1704:
1700:
1698:
1695:
1694:
1662:
1646:
1621:
1619:
1617:
1614:
1613:
1546:
1544:
1542:
1539:
1538:
1495:
1493:
1474:
1472:
1461:
1458:
1457:
1419:
1391:
1387:
1378:
1374:
1372:
1369:
1368:
1339:
1325:
1322:
1321:
1244:
1241:
1240:
1236:
1178:
1174:
1165:
1161:
1159:
1156:
1155:
1122:
1109:
1105:
1103:
1100:
1099:
1023:
1020:
1019:
1015:
989:
984:
981:
980:
951:
932:
928:
908:
904:
883:
879:
870:
866:
864:
861:
860:
826:
824:
820:
794:
792:
788:
753:
750:
749:
650:
646:
637:
633:
631:
628:
627:
603:
600:
599:
528:
524:
522:
519:
518:
486:
483:
482:
459:
445:
442:
441:
425:
422:
421:
356:
352:
350:
347:
346:
339:
324:interferometers
299:
291:
236:
218:
190:
97:
86:
80:
77:
69:help improve it
66:
57:
53:
46:
35:
28:
23:
22:
15:
12:
11:
5:
6960:
6950:
6949:
6947:Wave mechanics
6944:
6927:
6926:
6924:
6923:
6912:
6909:
6908:
6906:
6905:
6900:
6895:
6890:
6889:
6888:
6877:
6875:
6871:
6870:
6868:
6867:
6862:
6857:
6856:
6855:
6845:
6840:
6838:Casimir effect
6835:
6829:
6827:
6823:
6822:
6820:
6819:
6814:
6809:
6804:
6799:
6797:Quantum optics
6794:
6789:
6784:
6779:
6774:
6769:
6764:
6759:
6754:
6749:
6744:
6739:
6734:
6729:
6724:
6719:
6718:
6717:
6707:
6702:
6697:
6692:
6691:
6690:
6680:
6675:
6670:
6664:
6662:
6656:
6655:
6653:
6652:
6647:
6642:
6637:
6632:
6627:
6622:
6617:
6612:
6607:
6602:
6596:
6594:
6588:
6587:
6585:
6584:
6579:
6574:
6572:Quantum eraser
6569:
6564:
6559:
6554:
6549:
6544:
6539:
6534:
6528:
6526:
6522:
6521:
6519:
6518:
6513:
6508:
6503:
6498:
6493:
6488:
6487:
6486:
6485:
6484:
6469:
6464:
6459:
6454:
6449:
6443:
6441:
6435:
6434:
6432:
6431:
6426:
6421:
6416:
6411:
6405:
6403:
6399:
6398:
6396:
6395:
6390:
6385:
6380:
6375:
6370:
6365:
6359:
6357:
6353:
6352:
6350:
6349:
6348:
6347:
6342:
6332:
6327:
6322:
6317:
6312:
6307:
6302:
6297:
6292:
6287:
6282:
6277:
6272:
6271:
6270:
6265:
6260:
6255:
6245:
6243:Density matrix
6240:
6235:
6230:
6224:
6222:
6218:
6217:
6215:
6214:
6209:
6204:
6199:
6198:
6197:
6187:
6181:
6179:
6175:
6174:
6167:
6166:
6159:
6152:
6144:
6138:
6137:
6125:
6120:
6115:
6110:
6103:
6102:External links
6100:
6097:
6096:
6083:
6076:
6049:
6043:978-0525949695
6042:
6024:
5967:
5943:
5936:
5910:
5875:Optics Express
5861:
5826:
5819:
5811:Interferometry
5801:
5797:Phase contrast
5788:
5781:
5753:
5728:
5710:
5709:
5707:
5704:
5702:
5701:
5696:
5691:
5686:
5681:
5679:Newton's rings
5676:
5671:
5666:
5664:Lloyd's Mirror
5661:
5659:Interferometer
5656:
5651:
5646:
5641:
5636:
5631:
5626:
5620:
5618:
5615:
5606:. A vibrating
5598:, wavelength,
5583:
5580:
5523:Main article:
5520:
5517:
5445:Main article:
5442:
5439:
5436:Interferometry
5434:Main article:
5369:Main article:
5366:
5363:
5361:
5358:
5341:
5338:
5335:
5332:
5329:
5324:
5320:
5299:
5296:
5293:
5290:
5287:
5282:
5278:
5246:
5224:
5219:
5214:
5211:
5208:
5205:
5202:
5197:
5193:
5188:
5184:
5179:
5174:
5169:
5166:
5163:
5160:
5157:
5152:
5148:
5143:
5118:
5115:
5112:
5109:
5106:
5101:
5096:
5092:
5088:
5085:
5082:
5079:
5076:
5071:
5067:
5063:
5060:
5057:
5054:
5051:
5048:
5043:
5039:
5035:
5032:
5029:
5026:
5023:
5018:
5013:
5009:
4984:
4964:
4944:
4924:
4921:
4918:
4915:
4912:
4907:
4903:
4899:
4896:
4893:
4890:
4887:
4884:
4879:
4875:
4871:
4868:
4865:
4862:
4859:
4856:
4853:
4833:
4830:
4827:
4824:
4821:
4816:
4812:
4791:
4788:
4785:
4782:
4779:
4774:
4770:
4747:
4744:
4741:
4738:
4735:
4732:
4727:
4722:
4718:
4714:
4711:
4708:
4705:
4702:
4697:
4693:
4689:
4686:
4683:
4680:
4677:
4674:
4669:
4665:
4661:
4658:
4655:
4652:
4649:
4644:
4639:
4635:
4631:
4628:
4623:
4618:
4613:
4610:
4607:
4604:
4601:
4596:
4592:
4587:
4583:
4578:
4573:
4568:
4565:
4562:
4559:
4556:
4551:
4547:
4542:
4538:
4533:
4528:
4523:
4520:
4517:
4514:
4511:
4508:
4504:
4500:
4497:
4494:
4491:
4488:
4468:
4465:
4462:
4459:
4456:
4451:
4447:
4443:
4440:
4437:
4434:
4431:
4428:
4423:
4419:
4415:
4412:
4409:
4406:
4403:
4400:
4397:
4369:
4366:
4363:
4360:
4357:
4354:
4351:
4348:
4345:
4342:
4339:
4334:
4330:
4326:
4321:
4316:
4311:
4308:
4305:
4302:
4299:
4296:
4292:
4288:
4285:
4282:
4279:
4276:
4256:
4236:
4233:
4230:
4227:
4196:
4193:
4190:
4187:
4184:
4181:
4157:
4156:
4154:
4153:
4146:
4139:
4131:
4128:
4127:
4123:
4122:
4117:
4112:
4107:
4102:
4097:
4092:
4087:
4082:
4077:
4072:
4067:
4062:
4057:
4052:
4047:
4042:
4037:
4032:
4027:
4022:
4017:
4012:
4007:
4002:
3997:
3992:
3987:
3982:
3977:
3972:
3967:
3962:
3957:
3952:
3947:
3942:
3937:
3932:
3927:
3922:
3917:
3912:
3907:
3902:
3897:
3891:
3890:
3887:
3886:
3883:
3882:
3879:
3878:
3873:
3868:
3863:
3861:Density matrix
3858:
3853:
3848:
3843:
3838:
3833:
3827:
3824:
3823:
3820:
3819:
3815:
3814:
3809:
3804:
3799:
3794:
3789:
3784:
3783:
3782:
3781:
3780:
3765:
3760:
3755:
3750:
3745:
3739:
3738:
3733:
3732:
3729:
3728:
3724:
3723:
3718:
3713:
3708:
3703:
3697:
3696:
3693:
3692:
3689:
3688:
3684:
3683:
3678:
3673:
3668:
3663:
3658:
3652:
3651:
3650:
3644:
3641:
3640:
3637:
3636:
3632:
3631:
3626:
3621:
3615:
3614:
3613:
3612:
3611:
3609:Delayed-choice
3604:Quantum eraser
3599:
3598:
3593:
3588:
3583:
3578:
3573:
3568:
3563:
3558:
3553:
3547:
3546:
3543:
3542:
3539:
3538:
3534:
3533:
3532:
3531:
3521:
3516:
3511:
3506:
3501:
3496:
3494:Quantum number
3491:
3486:
3481:
3476:
3471:
3466:
3460:
3459:
3456:
3455:
3452:
3451:
3447:
3446:
3441:
3435:
3434:
3433:
3428:
3423:
3417:
3414:
3413:
3410:
3409:
3408:
3407:
3402:
3397:
3389:
3388:
3383:
3372:
3369:
3365:
3358:
3355:
3349:
3346:
3343:
3339:
3332:
3329:
3325:
3320:
3317:
3306:
3305:
3299:
3298:
3281:
3278:
3277:
3276:
3273:
3266:
3264:
3261:
3254:
3252:
3249:
3242:
3240:
3222:Lloyd's mirror
3194:
3191:
3156:
3153:
3118:
3115:
3112:
3108:
3104:
3099:
3095:
3091:
3088:
3084:
3080:
3075:
3071:
3067:
3064:
3061:
3056:
3052:
3048:
3043:
3039:
3035:
3031:
3027:
3022:
3018:
3012:
3009:
3006:
3002:
2998:
2993:
2989:
2985:
2982:
2978:
2974:
2969:
2965:
2961:
2958:
2954:
2950:
2947:
2923:
2920:
2917:
2913:
2909:
2904:
2900:
2896:
2893:
2889:
2885:
2880:
2876:
2872:
2869:
2866:
2863:
2859:
2855:
2850:
2846:
2842:
2838:
2834:
2829:
2825:
2821:
2818:
2815:
2811:
2807:
2802:
2797:
2793:
2789:
2786:
2782:
2778:
2773:
2768:
2764:
2760:
2757:
2754:
2750:
2747:
2744:
2740:
2736:
2731:
2727:
2723:
2720:
2717:
2713:
2709:
2706:
2703:
2700:
2697:
2693:
2689:
2686:
2656:
2651:
2648:
2645:
2642:
2639:
2635:
2631:
2626:
2622:
2618:
2615:
2611:
2607:
2603:
2599:
2594:
2590:
2586:
2581:
2578:
2575:
2572:
2569:
2565:
2561:
2556:
2552:
2548:
2545:
2541:
2537:
2533:
2529:
2524:
2520:
2516:
2513:
2510:
2507:
2503:
2499:
2496:
2451:
2448:
2445:
2442:
2439:
2435:
2431:
2426:
2422:
2418:
2415:
2411:
2407:
2403:
2399:
2394:
2390:
2386:
2383:
2380:
2377:
2373:
2369:
2364:
2360:
2338:
2335:
2332:
2329:
2326:
2322:
2318:
2313:
2309:
2305:
2302:
2298:
2294:
2290:
2286:
2281:
2277:
2273:
2270:
2267:
2264:
2260:
2256:
2251:
2247:
2192:
2189:
2188:
2187:
2184:
2177:
2162:wave functions
2142:
2139:
2109:
2102:
2098:
2095:
2089:
2085:
2062:
2059:
2052:
2048:
2044:
2040:
2036:
2031:
2028:
2025:
2020:
2017:
2014:
2010:
1987:
1982:
1978:
1975:
1969:
1964:
1961:
1958:
1954:
1950:
1945:
1941:
1920:
1917:
1914:
1911:
1908:
1888:
1885:
1882:
1862:
1838:
1834:
1830:
1826:
1822:
1792:
1791:Multiple beams
1789:
1768:
1765:
1747:
1727:
1724:
1721:
1717:
1712:
1707:
1703:
1677:
1674:
1669:
1666:
1661:
1658:
1653:
1650:
1645:
1642:
1637:
1633:
1630:
1627:
1624:
1597:
1594:
1591:
1588:
1585:
1582:
1579:
1576:
1573:
1570:
1567:
1562:
1558:
1555:
1552:
1549:
1522:
1517:
1513:
1510:
1507:
1504:
1501:
1498:
1492:
1487:
1483:
1480:
1477:
1471:
1468:
1465:
1418:
1415:
1414:
1413:
1402:
1399:
1394:
1390:
1386:
1381:
1377:
1355:
1352:
1349:
1346:
1342:
1338:
1335:
1332:
1329:
1309:
1306:
1303:
1300:
1296:
1293:
1290:
1286:
1283:
1279:
1276:
1273:
1269:
1266:
1263:
1260:
1257:
1254:
1251:
1248:
1230:
1219:
1216:
1213:
1210:
1207:
1204:
1201:
1198:
1195:
1192:
1189:
1186:
1181:
1177:
1173:
1168:
1164:
1143:
1140:
1136:
1132:
1129:
1125:
1121:
1118:
1115:
1112:
1108:
1087:
1084:
1081:
1078:
1075:
1072:
1069:
1066:
1063:
1060:
1057:
1054:
1051:
1048:
1045:
1042:
1039:
1036:
1033:
1030:
1027:
996:
992:
988:
968:
964:
958:
955:
950:
947:
944:
941:
938:
935:
931:
927:
924:
920:
915:
912:
907:
903:
900:
897:
894:
891:
886:
882:
878:
873:
869:
848:
844:
839:
835:
832:
829:
823:
819:
816:
812:
807:
803:
800:
797:
791:
787:
784:
781:
778:
775:
772:
769:
766:
763:
760:
757:
733:
730:
727:
724:
721:
718:
715:
712:
709:
706:
703:
700:
697:
694:
691:
688:
685:
682:
679:
676:
673:
670:
667:
664:
661:
658:
653:
649:
645:
640:
636:
607:
587:
584:
581:
578:
575:
572:
569:
566:
563:
560:
557:
554:
551:
548:
545:
542:
539:
536:
531:
527:
502:
499:
496:
493:
490:
466:
462:
458:
455:
452:
449:
429:
409:
406:
403:
400:
397:
394:
391:
388:
385:
382:
379:
376:
373:
370:
367:
364:
359:
355:
338:
335:
217:
214:
189:
186:
99:
98:
60:
58:
51:
26:
9:
6:
4:
3:
2:
6959:
6948:
6945:
6943:
6940:
6939:
6937:
6922:
6914:
6913:
6910:
6904:
6901:
6899:
6896:
6894:
6891:
6887:
6884:
6883:
6882:
6879:
6878:
6876:
6872:
6866:
6863:
6861:
6858:
6854:
6851:
6850:
6849:
6846:
6844:
6841:
6839:
6836:
6834:
6831:
6830:
6828:
6824:
6818:
6815:
6813:
6810:
6808:
6805:
6803:
6800:
6798:
6795:
6793:
6790:
6788:
6785:
6783:
6780:
6778:
6775:
6773:
6770:
6768:
6765:
6763:
6760:
6758:
6757:Quantum logic
6755:
6753:
6750:
6748:
6745:
6743:
6740:
6738:
6735:
6733:
6730:
6728:
6725:
6723:
6720:
6716:
6713:
6712:
6711:
6708:
6706:
6703:
6701:
6698:
6696:
6693:
6689:
6686:
6685:
6684:
6681:
6679:
6676:
6674:
6671:
6669:
6666:
6665:
6663:
6661:
6657:
6651:
6648:
6646:
6643:
6641:
6638:
6636:
6633:
6631:
6628:
6626:
6623:
6621:
6618:
6616:
6613:
6611:
6610:Quantum chaos
6608:
6606:
6603:
6601:
6598:
6597:
6595:
6593:
6589:
6583:
6580:
6578:
6577:Stern–Gerlach
6575:
6573:
6570:
6568:
6565:
6563:
6560:
6558:
6555:
6553:
6550:
6548:
6545:
6543:
6540:
6538:
6535:
6533:
6530:
6529:
6527:
6523:
6517:
6514:
6512:
6511:Transactional
6509:
6507:
6504:
6502:
6501:Quantum logic
6499:
6497:
6494:
6492:
6489:
6483:
6480:
6479:
6478:
6475:
6474:
6473:
6470:
6468:
6465:
6463:
6460:
6458:
6455:
6453:
6450:
6448:
6445:
6444:
6442:
6440:
6436:
6430:
6427:
6425:
6422:
6420:
6417:
6415:
6412:
6410:
6407:
6406:
6404:
6400:
6394:
6391:
6389:
6386:
6384:
6381:
6379:
6376:
6374:
6371:
6369:
6366:
6364:
6361:
6360:
6358:
6354:
6346:
6343:
6341:
6338:
6337:
6336:
6335:Wave function
6333:
6331:
6328:
6326:
6323:
6321:
6318:
6316:
6313:
6311:
6310:Superposition
6308:
6306:
6305:Quantum state
6303:
6301:
6298:
6296:
6293:
6291:
6288:
6286:
6283:
6281:
6278:
6276:
6273:
6269:
6266:
6264:
6261:
6259:
6258:Excited state
6256:
6254:
6251:
6250:
6249:
6246:
6244:
6241:
6239:
6236:
6234:
6231:
6229:
6226:
6225:
6223:
6219:
6213:
6210:
6208:
6205:
6203:
6200:
6196:
6193:
6192:
6191:
6188:
6186:
6183:
6182:
6180:
6176:
6172:
6165:
6160:
6158:
6153:
6151:
6146:
6145:
6142:
6136:
6132:
6129:
6126:
6124:
6121:
6119:
6116:
6114:
6111:
6109:
6106:
6105:
6093:
6087:
6079:
6073:
6069:
6065:
6064:
6059:
6058:Greene, Brian
6053:
6045:
6039:
6035:
6028:
6020:
6016:
6012:
6008:
6004:
6000:
5995:
5990:
5986:
5982:
5978:
5971:
5964:
5960:
5956:
5952:
5947:
5939:
5937:0-521-64222-1
5933:
5929:
5928:
5923:
5917:
5915:
5906:
5902:
5897:
5892:
5888:
5884:
5880:
5876:
5872:
5865:
5857:
5853:
5849:
5845:
5841:
5837:
5830:
5822:
5820:0-521-31162-4
5816:
5812:
5805:
5798:
5792:
5784:
5778:
5774:
5770:
5766:
5765:
5757:
5749:
5745:
5741:
5740:
5732:
5724:
5723:
5715:
5711:
5700:
5697:
5695:
5692:
5690:
5687:
5685:
5682:
5680:
5677:
5675:
5672:
5670:
5669:Moiré pattern
5667:
5665:
5662:
5660:
5657:
5655:
5652:
5650:
5647:
5645:
5642:
5640:
5637:
5635:
5632:
5630:
5627:
5625:
5622:
5621:
5614:
5611:
5609:
5605:
5601:
5597:
5593:
5589:
5579:
5577:
5573:
5569:
5568:optical fiber
5565:
5561:
5560:coaxial cable
5556:
5548:
5544:
5540:
5536:
5531:
5526:
5516:
5514:
5510:
5505:
5503:
5498:
5494:
5490:
5486:
5481:
5479:
5475:
5471:
5466:
5464:
5460:
5456:
5452:
5448:
5437:
5432:
5430:
5426:
5421:
5417:
5413:
5408:
5406:
5402:
5398:
5394:
5390:
5386:
5382:
5378:
5372:
5357:
5355:
5336:
5333:
5330:
5322:
5294:
5291:
5288:
5280:
5267:
5263:
5258:
5244:
5222:
5209:
5206:
5203:
5195:
5182:
5177:
5164:
5161:
5158:
5150:
5132:
5113:
5110:
5107:
5099:
5094:
5083:
5080:
5077:
5069:
5061:
5055:
5052:
5049:
5041:
5030:
5027:
5024:
5016:
5011:
4998:
4982:
4962:
4942:
4919:
4916:
4913:
4905:
4897:
4891:
4888:
4885:
4877:
4869:
4863:
4860:
4857:
4828:
4825:
4822:
4814:
4786:
4783:
4780:
4772:
4758:
4739:
4736:
4733:
4725:
4720:
4709:
4706:
4703:
4695:
4687:
4681:
4678:
4675:
4667:
4656:
4653:
4650:
4642:
4637:
4626:
4621:
4608:
4605:
4602:
4594:
4581:
4576:
4563:
4560:
4557:
4549:
4536:
4531:
4518:
4515:
4512:
4498:
4492:
4486:
4463:
4460:
4457:
4449:
4441:
4435:
4432:
4429:
4421:
4413:
4407:
4404:
4401:
4388:of two terms
4387:
4383:
4364:
4361:
4358:
4346:
4343:
4340:
4332:
4324:
4319:
4306:
4303:
4300:
4286:
4280:
4274:
4254:
4231:
4225:
4218:
4214:
4210:
4191:
4188:
4185:
4171:
4167:
4163:
4152:
4147:
4145:
4140:
4138:
4133:
4132:
4130:
4129:
4121:
4118:
4116:
4113:
4111:
4108:
4106:
4103:
4101:
4098:
4096:
4093:
4091:
4088:
4086:
4083:
4081:
4078:
4076:
4073:
4071:
4068:
4066:
4063:
4061:
4058:
4056:
4053:
4051:
4048:
4046:
4043:
4041:
4038:
4036:
4033:
4031:
4028:
4026:
4023:
4021:
4018:
4016:
4013:
4011:
4008:
4006:
4003:
4001:
3998:
3996:
3993:
3991:
3988:
3986:
3983:
3981:
3978:
3976:
3973:
3971:
3968:
3966:
3963:
3961:
3958:
3956:
3953:
3951:
3948:
3946:
3943:
3941:
3938:
3936:
3933:
3931:
3928:
3926:
3923:
3921:
3918:
3916:
3913:
3911:
3908:
3906:
3903:
3901:
3898:
3896:
3893:
3892:
3885:
3884:
3877:
3874:
3872:
3869:
3867:
3864:
3862:
3859:
3857:
3854:
3852:
3851:Quantum chaos
3849:
3847:
3844:
3842:
3839:
3837:
3834:
3832:
3829:
3828:
3822:
3821:
3813:
3810:
3808:
3807:Transactional
3805:
3803:
3800:
3798:
3797:Quantum logic
3795:
3793:
3790:
3788:
3785:
3779:
3776:
3775:
3774:
3771:
3770:
3769:
3766:
3764:
3761:
3759:
3756:
3754:
3751:
3749:
3746:
3744:
3741:
3740:
3736:
3731:
3730:
3722:
3719:
3717:
3714:
3712:
3709:
3707:
3704:
3702:
3699:
3698:
3691:
3690:
3682:
3679:
3677:
3674:
3672:
3669:
3667:
3664:
3662:
3659:
3657:
3654:
3653:
3649:
3646:
3645:
3639:
3638:
3630:
3627:
3625:
3622:
3620:
3617:
3616:
3610:
3607:
3606:
3605:
3602:
3601:
3597:
3594:
3592:
3589:
3587:
3584:
3582:
3579:
3577:
3574:
3572:
3569:
3567:
3564:
3562:
3559:
3557:
3554:
3552:
3549:
3548:
3541:
3540:
3530:
3527:
3526:
3525:
3524:Wave function
3522:
3520:
3517:
3515:
3512:
3510:
3507:
3505:
3504:Superposition
3502:
3500:
3497:
3495:
3492:
3490:
3487:
3485:
3482:
3480:
3477:
3475:
3472:
3470:
3467:
3465:
3462:
3461:
3454:
3453:
3445:
3442:
3440:
3437:
3436:
3432:
3429:
3427:
3424:
3422:
3419:
3418:
3412:
3411:
3406:
3403:
3401:
3398:
3396:
3393:
3392:
3391:
3390:
3386:
3353:
3347:
3330:
3327:
3323:
3315:
3308:
3307:
3304:
3301:
3300:
3296:
3295:
3291:
3287:
3270:
3265:
3258:
3253:
3246:
3241:
3238:
3237:
3236:
3234:
3230:
3225:
3223:
3219:
3214:
3212:
3208:
3204:
3203:beam splitter
3199:
3190:
3186:
3182:
3179:
3174:
3171:
3167:
3161:
3152:
3148:
3146:
3141:
3136:
3129:
3116:
3097:
3093:
3089:
3073:
3069:
3062:
3059:
3041:
3037:
3020:
3016:
3010:
3007:
2991:
2987:
2983:
2967:
2963:
2959:
2945:
2937:
2934:
2921:
2902:
2898:
2894:
2878:
2874:
2867:
2864:
2848:
2844:
2827:
2823:
2819:
2816:
2800:
2795:
2791:
2787:
2771:
2766:
2762:
2758:
2755:
2752:
2745:
2742:
2729:
2725:
2718:
2715:
2704:
2701:
2698:
2684:
2676:
2673:
2667:
2654:
2646:
2643:
2640:
2624:
2620:
2613:
2609:
2592:
2588:
2584:
2576:
2573:
2570:
2554:
2550:
2543:
2539:
2522:
2518:
2514:
2508:
2505:
2494:
2486:
2483:
2481:
2464:
2446:
2443:
2440:
2424:
2420:
2413:
2409:
2392:
2388:
2384:
2378:
2375:
2362:
2358:
2333:
2330:
2327:
2311:
2307:
2300:
2296:
2279:
2275:
2271:
2265:
2262:
2249:
2245:
2236:
2233:
2227:
2219:
2215:
2214:
2209:
2208:
2202:
2197:
2185:
2182:
2178:
2175:
2171:
2167:
2165:
2163:
2159:
2155:
2151:
2150:gravity waves
2147:
2138:
2136:
2132:
2127:
2125:
2120:
2107:
2100:
2096:
2093:
2087:
2083:
2073:
2060:
2057:
2050:
2046:
2042:
2038:
2034:
2029:
2026:
2023:
2018:
2015:
2012:
2008:
2000:To show that
1998:
1985:
1980:
1976:
1973:
1967:
1962:
1959:
1956:
1952:
1948:
1943:
1939:
1918:
1915:
1912:
1909:
1906:
1886:
1883:
1880:
1860:
1836:
1832:
1828:
1824:
1820:
1812:
1807:
1805:
1801:
1800:3-phase power
1796:
1788:
1785:
1782:
1773:
1764:
1761:
1755:
1750:
1741:
1725:
1722:
1719:
1715:
1710:
1705:
1701:
1692:
1688:
1675:
1672:
1667:
1664:
1659:
1656:
1651:
1648:
1643:
1640:
1635:
1631:
1628:
1625:
1622:
1611:
1608:
1595:
1592:
1589:
1586:
1583:
1580:
1577:
1574:
1571:
1568:
1565:
1560:
1556:
1553:
1550:
1547:
1536:
1533:
1520:
1515:
1511:
1508:
1505:
1502:
1499:
1496:
1490:
1485:
1481:
1478:
1475:
1469:
1466:
1455:
1453:
1449:
1445:
1440:
1431:
1423:
1400:
1397:
1392:
1388:
1384:
1379:
1375:
1353:
1350:
1344:
1340:
1336:
1330:
1327:
1307:
1304:
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1127:
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722:
719:
716:
713:
710:
707:
704:
698:
695:
692:
686:
683:
680:
677:
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656:
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638:
634:
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494:
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480:
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450:
447:
427:
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398:
395:
392:
386:
383:
380:
377:
371:
368:
365:
357:
353:
344:
334:
332:
327:
325:
321:
317:
316:laser speckle
313:
307:
303:
297:
289:
288:even multiple
285:
275:
271:
268:
264:
260:
256:
230:
222:
213:
211:
207:
203:
199:
195:
185:
183:
179:
178:gravity waves
175:
171:
167:
163:
159:
158:
153:
152:
147:
146:
141:
138:
134:
130:
122:
118:
114:
110:
105:
95:
92:
84:
81:February 2022
74:
70:
64:
61:This article
59:
50:
49:
44:
40:
39:Moiré pattern
33:
19:
6942:Interference
6640:Quantum mind
6552:Franck–Hertz
6414:Klein–Gordon
6363:Formulations
6356:Formulations
6285:Interference
6284:
6275:Entanglement
6253:Ground state
6248:Energy level
6221:Fundamentals
6185:Introduction
6091:
6086:
6062:
6052:
6033:
6027:
5984:
5980:
5970:
5946:
5925:
5878:
5874:
5864:
5839:
5835:
5829:
5810:
5804:
5791:
5763:
5756:
5738:
5731:
5721:
5714:
5612:
5585:
5552:
5506:
5482:
5467:
5455:Thomas Young
5453:
5450:
5409:
5396:
5385:interference
5380:
5374:
5360:Applications
5266:matter waves
5259:
4996:
4759:
4209:wavefunction
4168:– resembles
4161:
4160:
3706:Klein–Gordon
3642:Formulations
3479:Energy level
3474:Entanglement
3457:Fundamentals
3444:Interference
3443:
3395:Introduction
3262:An oil spill
3226:
3215:
3200:
3196:
3187:
3183:
3175:
3162:
3158:
3149:
3140:polarization
3137:
3130:
2938:
2935:
2677:
2675:is given by
2671:
2668:
2487:
2484:
2465:
2237:
2231:
2223:
2217:
2212:
2211:
2206:
2205:
2201:optical flat
2158:matter waves
2144:
2128:
2121:
2074:
1999:
1808:
1797:
1794:
1786:
1781:point source
1778:
1762:
1745:
1742:
1693:
1689:
1612:
1609:
1537:
1534:
1456:
1454:is given by
1451:
1447:
1443:
1436:
1232:
1011:
340:
331:matter waves
328:
308:
304:
296:odd multiple
295:
287:
281:
252:
210:Thomas Young
205:
201:
194:interference
193:
191:
182:matter waves
156:
155:
150:
149:
143:
133:interference
132:
126:
120:
117:Out of phase
112:
87:
78:
62:
6898:EPR paradox
6678:Quantum bus
6547:Double-slit
6525:Experiments
6491:Many-worlds
6429:Schrödinger
6393:Phase space
6383:Schrödinger
6373:Interaction
6330:Uncertainty
6300:Nonlocality
6295:Measurement
6290:Decoherence
6280:Hamiltonian
5639:Diffraction
5509:slip gauges
5502:calibration
5393:frequencies
5354:matter wave
4217:probability
4095:von Neumann
4080:Schrödinger
3856:EPR paradox
3787:Many-worlds
3721:Schrödinger
3676:Schrödinger
3671:Phase-space
3661:Interaction
3566:Double-slit
3544:Experiments
3519:Uncertainty
3489:Nonlocality
3484:Measurement
3469:Decoherence
3439:Hamiltonian
3290:Matter wave
3229:iridescence
2220:, are seen.
1873:waves from
1439:plane waves
6936:Categories
6826:Extensions
6660:Technology
6506:Relational
6457:Copenhagen
6368:Heisenberg
6315:Tunnelling
6178:Background
5955:Leighton R
5706:References
5600:absorption
5543:telescopes
5405:difference
4090:Sommerfeld
4005:Heisenberg
4000:Gutzwiller
3940:de Broglie
3888:Scientists
3802:Relational
3753:Copenhagen
3656:Heisenberg
3514:Tunnelling
3415:Background
3284:See also:
3178:laser beam
2146:Mechanical
1754:wavelength
744:Using the
479:wavenumber
343:sinusoidal
278:thickness.
263:vector sum
216:Mechanisms
6532:Bell test
6402:Equations
6228:Born rule
6011:1367-2630
5994:1210.6243
5951:Feynman R
5922:Born, Max
5836:Phys. Rev
5604:impedance
5564:waveguide
5489:Michelson
5397:perceived
5377:acoustics
5319:Ψ
5277:Ψ
5192:Ψ
5147:Ψ
5100:∗
5091:Ψ
5066:Ψ
5038:Ψ
5017:∗
5008:Ψ
4902:Ψ
4874:Ψ
4852:Ψ
4811:Ψ
4769:Ψ
4760:Usually,
4726:∗
4717:Ψ
4692:Ψ
4664:Ψ
4643:∗
4634:Ψ
4591:Ψ
4546:Ψ
4507:Ψ
4446:Ψ
4418:Ψ
4396:Ψ
4353:Ψ
4333:∗
4329:Ψ
4295:Ψ
4180:Ψ
4120:Zeilinger
3965:Ehrenfest
3694:Equations
3371:⟩
3368:Ψ
3357:^
3345:⟩
3342:Ψ
3319:ℏ
3094:φ
3090:−
3070:φ
3063:
2899:φ
2895:−
2875:φ
2868:
2759:∝
2730:∗
2702:∫
2644:ω
2641:−
2621:φ
2574:ω
2571:−
2551:φ
2444:ω
2441:−
2421:φ
2331:ω
2328:−
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2226:intensity
2097:π
2047:φ
2027:−
2009:∑
1977:π
1960:−
1953:φ
1949:−
1940:φ
1916:−
1833:φ
1726:θ
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1716:λ
1676:…
1660:±
1644:±
1636:λ
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1629:
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1575:±
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1500:π
1486:λ
1479:π
1467:φ
1464:Δ
1337:φ
1331:
1308:…
1302:π
1292:π
1282:π
1275:π
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1120:φ
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1086:…
1080:π
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1038:−
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1026:φ
987:φ
954:φ
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940:−
926:
911:φ
902:
818:
799:−
786:
771:
759:
723:φ
714:ω
711:−
699:
684:ω
681:−
669:
624:superpose
606:φ
583:φ
574:ω
571:−
559:
498:π
489:ω
465:λ
457:π
402:ω
399:−
387:
259:amplitude
212:in 1801.
192:The word
188:Etymology
6921:Category
6715:Timeline
6467:Ensemble
6447:Bayesian
6340:Collapse
6212:Glossary
6195:Timeline
6131:Archived
6060:(1999).
5959:Sands M.
5905:25401860
5617:See also
5596:velocity
4045:Millikan
3970:Einstein
3955:Davisson
3910:Blackett
3895:Aharonov
3763:Ensemble
3743:Bayesian
3648:Overview
3529:Collapse
3509:Symmetry
3400:Glossary
3209:and the
2181:coherent
1931:, where
1802:and the
170:acoustic
137:coherent
109:In phase
6874:Related
6853:History
6592:Science
6424:Rydberg
6190:History
5883:Bibcode
5844:Bibcode
5608:crystal
5493:cadmium
5420:tremolo
4085:Simmons
4075:Rydberg
4040:Moseley
4020:Kramers
4010:Hilbert
3995:Glauber
3990:Feynman
3975:Everett
3945:Compton
3716:Rydberg
3405:History
3166:sodium-
2174:complex
2154:optical
1811:phasors
620:radians
513:is the
477:is the
129:physics
67:Please
6567:Popper
6074:
6068:97–109
6040:
6019:832961
6017:
6009:
5957:, and
5934:
5903:
5817:
5779:
5699:Upfade
5416:unison
5412:tuning
5401:volume
5389:sounds
5383:is an
4172:. Let
4115:Zeeman
4110:Wigner
4060:Planck
4030:Landau
4015:Jordan
3666:Matrix
3596:Popper
2466:where
598:where
420:where
200:words
6477:Local
6419:Pauli
6409:Dirac
6015:S2CID
5989:arXiv
5602:, or
5537:, an
5410:With
4999:, is
4207:be a
4070:Raman
4055:Pauli
4050:Onnes
3985:Fermi
3960:Debye
3950:Dirac
3915:Bloch
3905:Bethe
3773:Local
3711:Pauli
3701:Dirac
3499:State
1320:then
1098:then
284:phase
267:crest
202:inter
198:Latin
180:, or
166:radio
162:light
140:waves
6072:ISBN
6038:ISBN
6007:ISSN
5932:ISBN
5901:PMID
5815:ISBN
5777:ISBN
5533:The
5381:beat
5379:, a
5365:Beat
4802:and
4105:Wien
4100:Weyl
4065:Rabi
4035:Laue
4025:Lamb
3980:Fock
3935:Bose
3930:Born
3925:Bohr
3920:Bohm
3900:Bell
3288:and
3231:and
3220:and
2235:is:
2170:real
2156:and
2148:and
2122:The
1853:for
1743:and
481:and
322:and
253:The
206:fere
5999:doi
5891:doi
5852:doi
5840:159
5769:doi
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5592:gas
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2865:cos
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1328:cos
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1111:cos
923:cos
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783:cos
768:cos
756:cos
696:cos
666:cos
556:cos
384:cos
326:.
298:of
290:of
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