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5446:'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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5567:. 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.
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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
5411:
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
3177:
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
294:
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
3139:
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
3148:
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
5488:
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.
3173:
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.
3169:
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
258:
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
298:
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
1772:
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
3224:. 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.
3131:
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
3140:
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
291:. 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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5788:. 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,
1604:
2916:{\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.
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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
4924:
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.
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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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4740:{\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))}
3300:
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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
6351:
5563:. Interferometry increases the total signal collected, but its primary purpose is to vastly increase the resolution through a process called
3636:
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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.
3124:. 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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1992:
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149:) 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
1798:
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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31:
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5714:. University College London (UCL) UCL Library Services. London : printed by W. Bulmer and Co., Cleveland Row, St. James's.
5125:
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Interference of right traveling (green) and left traveling (blue) waves in Two-dimensional space, resulting in final (red) wave
4836:
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3111:{\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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79:
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On the mechanism of the eye / by Thomas Young.; Young, Thomas; University
College, London Library Services (1801).
5341:. The interference pattern occurs on the far side, observed by detectors suitable to the particles originating the
3472:
1359:
961:{\displaystyle W_{1}+W_{2}=2A\cos \left({\varphi \over 2}\right)\cos \left(kx-\omega t+{\varphi \over 2}\right).}
243:
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5420:, 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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4373:. 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.
1312:
108:: (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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1515:{\displaystyle \Delta \varphi ={\frac {2\pi d}{\lambda }}={\frac {2\pi x\sin \theta }{\lambda }}.}
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1670:{\displaystyle {\frac {x\sin \theta }{\lambda }}=\pm {\frac {1}{2}},\pm {\frac {3}{2}},\ldots }
734:
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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
2153:. Some of the differences between real valued and complex valued wave interference include:
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5476:. 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
1891:
841:{\textstyle \cos a+\cos b=2\cos \left({a-b \over 2}\right)\cos \left({a+b \over 2}\right),}
131:
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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5246:, then there is no quantum mechanical interference associated with situations A and B.
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2649:{\displaystyle U(\mathbf {r} ,t)=A_{1}(\mathbf {r} )e^{i}+A_{2}(\mathbf {r} )e^{i}.}
1795:. In both of these cases, the result is achieved by uniform spacing of the phases.
318:
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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100:: 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
5451:
5111:{\displaystyle \Psi _{A}^{*}(x,t)\Psi _{B}(x,t)+\Psi _{A}(x,t)\Psi _{B}^{*}(x,t)}
4108:
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Any two different real waves in the same medium interfere; complex waves must be
2134:
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Pfleegor, R. L.; Mandel, L. (1967). "Interference of independent photon beams".
5579:
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
1410:
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is known as the fringe spacing. The fringe spacing increases with increase in
312:
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1302:{\displaystyle \varphi =\ldots ,-3\pi ,\,-\pi ,\,\pi ,\,3\pi ,\,5\pi ,\ldots }
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3365:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }
3191:
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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).
283:(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
1590:{\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
1080:{\displaystyle \varphi =\ldots ,-4\pi ,-2\pi ,0,2\pi ,4\pi ,\ldots }
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331:
97:
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209:
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1143:, 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
5687:
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2141:
can be directly observed: they are real-valued wave functions;
2064:
one merely assumes the converse, then multiplies both sides by
1980:{\displaystyle \varphi _{n}-\varphi _{n-1}={\frac {2\pi }{N}}.}
1799:
608:
26:"Interference pattern" redirects here. For Moiré patterns, see
4362:{\displaystyle P(x)=|\Psi (x,t)|^{2}=\Psi ^{*}(x,t)\Psi (x,t)}
2446:{\displaystyle U_{2}(\mathbf {r} ,t)=A_{2}(\mathbf {r} )e^{i}}
2333:{\displaystyle U_{1}(\mathbf {r} ,t)=A_{1}(\mathbf {r} )e^{i}}
6023:
This is Your Brain on Music: The
Science of a Human Obsession
5377:
186:
3216:
Interference can also be seen in everyday phenomena such as
1760:
5858:
Patel, R.; Achamfuo-Yeboah, S.; Light R.; Clark M. (2014).
128:
3170:
spurious interference fringes which can result in errors.
5580:
5472:
Interferometry has been used in defining and calibrating
5219:{\displaystyle |\Psi _{A}(x,t)|^{2}+|\Psi _{B}(x,t)|^{2}}
1426:
A simple form of interference pattern is obtained if two
5504:. It is also used in the testing of optical components.
5489:
Interferometry is still fundamental in establishing the
4917:{\displaystyle \Psi (x,t)=\Psi _{A}(x,t)+\Psi _{B}(x,t)}
4461:{\displaystyle \Psi (x,t)=\Psi _{A}(x,t)+\Psi _{B}(x,t)}
16:
Phenomenon resulting from the superposition of two waves
5485:
5345:. The pattern matches the optical double slit pattern.
1414:
Geometrical arrangement for two plane wave interference
5249:
The best known example of quantum interference is the
1723:{\displaystyle d_{f}={\frac {\lambda }{\sin \theta }}}
743:
580:{\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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2055:{\displaystyle \sum _{n=0}^{N-1}Ae^{i\varphi _{n}}=0}
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1362:
1315:
1234:
1149:
1093:
1013:
974:
854:
621:
593:
512:
476:
435:
415:
340:
5963:
1524:
It can be seen that the two waves are in phase when
52:
may be too technical for most readers to understand
5333:
5291:
5238:
5218:
5110:
4976:
4956:
4936:
4916:
4825:
4783:
4739:
4460:
4361:
4248:
4228:
4188:
3364:
3110:
2915:
2648:
2445:
2332:
2101:
2054:
1979:
1912:
1880:
1854:
1834:
1722:
1669:
1589:
1514:
1394:
1348:
1301:
1211:
1135:
1079:
988:
960:
840:
725:
599:
579:
494:
458:
421:
401:
5753:History of the Principle of Interference of Light
1003:: If the phase difference is an even multiple of
137:. The resultant wave may have greater intensity (
6922:
6112:Java simulation of interference of water waves 2
6107:Java simulation of interference of water waves 1
5731:. Oxford Music Online. Oxford University Press.
2129:
2115:uses interference between multiple reflections.
1224:: If the phase difference is an odd multiple of
334:wave traveling to the right along the x-axis is
254:of the amplitudes of the individual waves. If a
173:as well as in loudspeakers as electrical waves.
5950:, The Feynman Lectures Website, September 2013.
5905:
5903:
1422:Interference fringes in overlapping plane waves
1212:{\displaystyle W_{1}+W_{2}=2A\cos(kx-\omega t)}
1136:{\displaystyle \left|\cos(\varphi /2)\right|=1}
5822:
2459:represents the magnitude of the displacement,
1755:
19:For interference in radio communications, see
6144:
5966:"Controlled double-slit electron diffraction"
5952:"The Feynman Lectures on Physics, Volume III"
5496:Interferometry is used in the calibration of
4131:
3127:Classically the two waves must have the same
607:is the phase difference between the waves in
402:{\displaystyle W_{1}(x,t)=A\cos(kx-\omega t)}
325:
221:Interference of waves from two point sources.
5900:
4944:is the probability of finding the object at
3359:
3333:
3228:Iridiscence caused by thin-film interference
3202:are examples of amplitude-division systems.
3143:
2179:
1435:, then the relative phase changes along the
6117:Flash animations demonstrating interference
6039:
5412:beating starts to sound like a note, and a
6151:
6137:
6102:Expressions of position and fringe spacing
5570:
4204:for a quantum mechanical object. Then the
4138:
4124:
3263:White light interference in a soap bubble.
1405:
271:Constructive interference occurs when the
5981:
5919:. Cambridge: Cambridge University Press.
5883:
5802:. Cambridge: Cambridge University Press.
5429:
4158:
2740:
1439:-axis. The phase difference at the point
1345:
1286:
1276:
1269:
1259:
80:Learn how and when to remove this message
64:, without removing the technical details.
5909:
5517:
2474:The displacement of the summed waves is
2183:
2102:{\displaystyle e^{i{\frac {2\pi }{N}}}.}
1759:
1417:
1409:
261:
224:
216:
208:
91:
6020:
5737:10.1093/gmo/9781561592630.article.20622
5507:
5500:(called gauge blocks in the US) and in
3268:
3181:
2188:Creation of interference fringes by an
1599:and are half a cycle out of phase when
32:Interference pattern (electromyography)
6923:
6045:
5749:
1356:, so the sum of the two waves is zero
6158:
6132:
5797:
5724:
3239:Smartphone with iridescent back panel
615:and add: the sum of the two waves is
62:make it understandable to non-experts
5860:"Widefield two laser interferometry"
4236:of observing the object at position
1349:{\displaystyle \cos(\varphi /2)=0\,}
36:
3190:In an amplitude-division system, a
275:difference between the waves is an
244:principle of superposition of waves
13:
6055:. New York: W.W. Norton. pp.
5307:
5265:
5180:
5135:
5079:
5054:
5026:
4996:
4890:
4862:
4840:
4799:
4757:
4705:
4680:
4652:
4622:
4579:
4534:
4495:
4434:
4406:
4384:
4341:
4317:
4283:
4168:
3670:Sum-over-histories (path integral)
3356:
3330:
3286:Part of a series of articles about
3207:Young's double slit interferometer
1835:{\displaystyle Ae^{i\varphi _{n}}}
1802:, each wave can be represented as
1452:
14:
6947:
6090:
5118:in the above equation. As in the
3307:
1779:
6905:
6904:
3256:
3244:
3232:
3095:
3071:
3039:
3018:
2989:
2965:
2941:
2900:
2876:
2846:
2825:
2798:
2769:
2727:
2700:
2680:
2622:
2590:
2552:
2520:
2490:
2422:
2390:
2360:
2309:
2277:
2247:
459:{\displaystyle k=2\pi /\lambda }
322:also demonstrate interference.
41:
6081:Geometrical and Physical Optics
6073:
6014:
5348:
5119:
96:The interference of two waves.
6854:Relativistic quantum mechanics
5933:
5851:
5816:
5791:
5778:
5743:
5718:
5701:
5334:{\displaystyle \Psi _{B}(x,t)}
5328:
5316:
5292:{\displaystyle \Psi _{A}(x,t)}
5286:
5274:
5206:
5201:
5189:
5175:
5161:
5156:
5144:
5130:
5105:
5093:
5075:
5063:
5047:
5035:
5022:
5010:
4911:
4899:
4883:
4871:
4855:
4843:
4826:{\displaystyle \Psi _{B}(x,t)}
4820:
4808:
4784:{\displaystyle \Psi _{A}(x,t)}
4778:
4766:
4734:
4731:
4719:
4701:
4689:
4673:
4661:
4648:
4636:
4618:
4605:
4600:
4588:
4574:
4560:
4555:
4543:
4529:
4515:
4510:
4498:
4491:
4484:
4478:
4455:
4443:
4427:
4415:
4399:
4387:
4356:
4344:
4338:
4326:
4303:
4298:
4286:
4279:
4272:
4266:
4223:
4217:
4183:
4171:
3820:Relativistic quantum mechanics
3352:
3345:
3326:
3102:
3099:
3091:
3075:
3067:
3054:
3043:
3035:
3022:
3014:
2993:
2985:
2969:
2961:
2945:
2937:
2907:
2904:
2896:
2880:
2872:
2859:
2850:
2842:
2829:
2821:
2802:
2794:
2773:
2765:
2737:
2723:
2710:
2696:
2684:
2676:
2658:The intensity of the light at
2638:
2626:
2618:
2605:
2594:
2586:
2568:
2556:
2548:
2535:
2524:
2516:
2500:
2486:
2438:
2426:
2418:
2405:
2394:
2386:
2370:
2356:
2325:
2313:
2305:
2292:
2281:
2273:
2257:
2243:
1336:
1322:
1206:
1188:
1119:
1105:
726:{\displaystyle W_{1}+W_{2}=A.}
717:
714:
690:
678:
660:
651:
574:
550:
535:
523:
495:{\displaystyle \omega =2\pi f}
396:
378:
363:
351:
250:at that point is equal to the
1:
6832:Quantum statistical mechanics
6609:Quantum differential calculus
6531:Delayed-choice quantum eraser
6314:Symmetry in quantum mechanics
5992:10.1088/1367-2630/15/3/033018
5976:(3). IOP Publishing: 033018.
5694:
5502:coordinate-measuring machines
5493:chain in length measurement.
3860:Quantum statistical mechanics
2130:Complex valued wave functions
1395:{\displaystyle W_{1}+W_{2}=0}
204:
124:is a phenomenon in which two
5683:Rayleigh roughness criterion
5542:In 1946, a technique called
2124:interference vs. diffraction
1745:, and with decreasing angle
737:for the sum of two cosines:
176:
30:. For the medical term, see
21:Interference (communication)
7:
6634:Quantum stochastic calculus
6624:Quantum measurement problem
6546:Mach–Zehnder interferometer
6021:Levitin, Daniel J. (2006).
5605:
5544:astronomical interferometry
5514:Astronomical interferometer
5459:Michelson–Morley experiment
5388:as a periodic variation in
3830:Quantum information science
3200:Mach–Zehnder interferometer
1756:Between two spherical waves
102:(constructive interference)
10:
6952:
5725:Jones, Peter Ward (2001).
5511:
5433:
5422:
5357:
4189:{\displaystyle \Psi (x,t)}
3272:
2113:Fabry–Pérot interferometer
989:{\displaystyle \varphi /2}
326:Real-valued wave functions
193:which means "between" and
110:(destructive interference)
25:
18:
6900:
6862:
6814:
6694:Quantum complexity theory
6672:Quantum cellular automata
6647:
6579:
6513:
6426:
6390:
6377:Path integral formulation
6344:
6209:
6166:
6083:, 1968, Longmans, London.
5762:10.1007/978-3-0348-8652-9
5530:formed from many smaller
4986:quantum interference term
3162:successful applications.
3144:Light source requirements
2463:represents the phase and
2180:Optical wave interference
1001:Constructive interference
140:constructive interference
6761:Quantum machine learning
6741:Quantum key distribution
6731:Quantum image processing
6721:Quantum error correction
6571:Wheeler's delayed choice
5845:10.1103/physrev.159.1084
5711:Young, Thomas, 1773-1829
5638:Interference lithography
5396:of the two frequencies.
3865:Quantum machine learning
3618:Wheeler's delayed-choice
3196:Michelson interferometer
2126:for further discussion.
1222:Destructive interference
600:{\displaystyle \varphi }
309:anti-reflective coatings
146:destructive interference
6677:Quantum finite automata
5728:Oxford University Press
5643:Interference visibility
5577:acoustic interferometer
5571:Acoustic interferometry
5353:
5299:and the other becomes
4155:wave-behavior of matter
3575:Leggett–Garg inequality
1406:Between two plane waves
429:is the peak amplitude,
6781:Quantum neural network
6025:. Dutton. p. 22.
5970:New Journal of Physics
5750:Kipnis, Nahum (1991).
5678:Thin-film interference
5663:Multipath interference
5539:
5436:Optical interferometry
5430:Optical interferometry
5380:of slightly different
5335:
5293:
5253:. In this experiment,
5251:double-slit experiment
5240:
5220:
5112:
4978:
4958:
4938:
4918:
4827:
4785:
4741:
4462:
4363:
4250:
4230:
4190:
3366:
3275:Double-slit experiment
3112:
2917:
2650:
2447:
2334:
2210:
2155:
2103:
2056:
2022:
1981:
1914:
1882:
1856:
1836:
1765:
1724:
1671:
1591:
1516:
1423:
1415:
1396:
1350:
1303:
1213:
1137:
1081:
990:
962:
842:
735:trigonometric identity
727:
611:. The two waves will
601:
581:
496:
460:
423:
403:
301:double-slit experiment
268:
239:
222:
214:
143:) or lower amplitude (
113:
6806:Quantum teleportation
6334:Wave–particle duality
5913:; Wolf, Emil (1999).
5798:Steel, W. H. (1986).
5528:interferometric array
5521:
5448:wave–particle duality
5336:
5294:
5241:
5221:
5113:
4979:
4959:
4939:
4919:
4828:
4786:
4742:
4463:
4364:
4251:
4231:
4191:
3560:Elitzur–Vaidman
3550:Davisson–Germer
3367:
3222:structural coloration
3113:
2918:
2651:
2448:
2335:
2187:
2104:
2057:
1996:
1982:
1915:
1913:{\displaystyle n=N-1}
1883:
1857:
1837:
1763:
1725:
1672:
1592:
1517:
1421:
1413:
1397:
1351:
1304:
1214:
1138:
1082:
991:
963:
843:
728:
602:
582:
497:
461:
424:
404:
265:
237:
220:
212:
95:
6837:Quantum field theory
6766:Quantum metamaterial
6711:Quantum cryptography
6441:Consistent histories
5916:Principles of Optics
5885:10.1364/OE.22.027094
5613:Active noise control
5508:Radio interferometry
5376:pattern between two
5303:
5261:
5230:
5126:
4992:
4968:
4948:
4928:
4837:
4795:
4753:
4472:
4381:
4375:linear superposition
4260:
4240:
4229:{\displaystyle P(x)}
4211:
4202:Schrödinger equation
4165:
4159:optical interference
4151:Quantum interference
3825:Quantum field theory
3737:Consistent histories
3374:Schrödinger equation
3301:
3269:Quantum interference
3182:Optical arrangements
2931:
2670:
2480:
2343:
2230:
2207:interference fringes
2068:
1993:
1924:
1892:
1866:
1846:
1806:
1686:
1605:
1530:
1449:
1360:
1313:
1232:
1147:
1091:
1011:
972:
852:
848:this can be written
741:
619:
591:
510:
474:
433:
413:
338:
185:is derived from the
6822:Quantum fluctuation
6791:Quantum programming
6751:Quantum logic gates
6736:Quantum information
6716:Quantum electronics
6191:Classical mechanics
5876:2014OExpr..2227094P
5870:(22): 27094–27101.
5837:1967PhRv..159.1084P
5673:Optical path length
5623:Coherence (physics)
5559:, or other type of
5534:, like many larger
5463:luminiferous aether
5457:The results of the
5418:missing fundamental
5120:classical wave case
5092:
5009:
4718:
4635:
4371:complex conjugation
3613:Stern–Gerlach
3410:Classical mechanics
3159:mercury-vapor lamps
2793:
2764:
2120:diffraction grating
1881:{\displaystyle n=0}
1793:diffraction grating
163:surface water waves
6875:in popular culture
6657:Quantum algorithms
6505:Von Neumann–Wigner
6485:Objective collapse
6196:Old quantum theory
6122:2009-06-24 at the
5565:Aperture synthesis
5540:
5467:special relativity
5392:whose rate is the
5331:
5289:
5236:
5216:
5108:
5078:
4995:
4974:
4954:
4934:
4914:
4823:
4781:
4737:
4704:
4621:
4458:
4369:where * indicates
4359:
4246:
4226:
4186:
3801:Von Neumann–Wigner
3781:Objective-collapse
3580:Mach–Zehnder
3570:Leggett inequality
3565:Franck–Hertz
3415:Old quantum theory
3362:
3134:polarization state
3108:
2913:
2779:
2750:
2646:
2443:
2330:
2211:
2099:
2052:
1977:
1910:
1878:
1852:
1832:
1766:
1720:
1667:
1587:
1512:
1424:
1416:
1392:
1346:
1299:
1209:
1133:
1077:
986:
958:
838:
723:
597:
577:
492:
456:
419:
399:
269:
240:
223:
215:
114:
6918:
6917:
6892:Quantum mysticism
6870:Schrödinger's cat
6801:Quantum simulator
6771:Quantum metrology
6699:Quantum computing
6662:Quantum amplifier
6639:Quantum spacetime
6604:Quantum cosmology
6594:Quantum chemistry
6309:Scattering theory
6257:Zero-point energy
6252:Degenerate levels
6160:Quantum mechanics
6066:978-0-393-04688-5
5771:978-3-0348-9717-4
5633:Haidinger fringes
5561:transmission line
5239:{\displaystyle x}
4977:{\displaystyle x}
4957:{\displaystyle x}
4937:{\displaystyle x}
4249:{\displaystyle x}
4148:
4147:
3855:Scattering theory
3835:Quantum computing
3608:Schrödinger's cat
3540:Bell's inequality
3348:
3323:
3292:Quantum mechanics
3046:
2469:angular frequency
2092:
1972:
1855:{\displaystyle N}
1718:
1659:
1643:
1627:
1552:
1507:
1477:
948:
905:
829:
797:
504:angular frequency
422:{\displaystyle A}
235:
90:
89:
82:
6943:
6908:
6907:
6619:Quantum geometry
6614:Quantum dynamics
6471:Superdeterminism
6367:Matrix mechanics
6222:Bra–ket notation
6153:
6146:
6139:
6130:
6129:
6084:
6077:
6071:
6070:
6043:
6037:
6036:
6018:
6012:
6011:
5985:
5961:
5955:
5954:(online edition)
5937:
5931:
5930:
5907:
5898:
5897:
5887:
5855:
5849:
5848:
5831:(5): 1084–1088.
5820:
5814:
5813:
5795:
5789:
5784:Ockenga, Wymke.
5782:
5776:
5775:
5747:
5741:
5740:
5722:
5716:
5715:
5705:
5618:Beat (acoustics)
5583:or liquid, such
5536:radio telescopes
5524:Very Large Array
5474:length standards
5465:and in favor of
5414:combination tone
5360:Beat (acoustics)
5340:
5338:
5337:
5332:
5315:
5314:
5298:
5296:
5295:
5290:
5273:
5272:
5245:
5243:
5242:
5237:
5225:
5223:
5222:
5217:
5215:
5214:
5209:
5188:
5187:
5178:
5170:
5169:
5164:
5143:
5142:
5133:
5117:
5115:
5114:
5109:
5091:
5086:
5062:
5061:
5034:
5033:
5008:
5003:
4983:
4981:
4980:
4975:
4963:
4961:
4960:
4955:
4943:
4941:
4940:
4935:
4923:
4921:
4920:
4915:
4898:
4897:
4870:
4869:
4832:
4830:
4829:
4824:
4807:
4806:
4790:
4788:
4787:
4782:
4765:
4764:
4746:
4744:
4743:
4738:
4717:
4712:
4688:
4687:
4660:
4659:
4634:
4629:
4614:
4613:
4608:
4587:
4586:
4577:
4569:
4568:
4563:
4542:
4541:
4532:
4524:
4523:
4518:
4494:
4467:
4465:
4464:
4459:
4442:
4441:
4414:
4413:
4368:
4366:
4365:
4360:
4325:
4324:
4312:
4311:
4306:
4282:
4255:
4253:
4252:
4247:
4235:
4233:
4232:
4227:
4200:solution of the
4195:
4193:
4192:
4187:
4140:
4133:
4126:
3767:Superdeterminism
3420:Bra–ket notation
3371:
3369:
3368:
3363:
3355:
3350:
3349:
3341:
3329:
3324:
3322:
3311:
3283:
3282:
3260:
3248:
3236:
3123:
3117:
3115:
3114:
3109:
3098:
3090:
3089:
3074:
3066:
3065:
3047:
3042:
3034:
3033:
3021:
3013:
3012:
3003:
2992:
2984:
2983:
2968:
2960:
2959:
2944:
2922:
2920:
2919:
2914:
2903:
2895:
2894:
2879:
2871:
2870:
2849:
2841:
2840:
2828:
2820:
2819:
2801:
2792:
2787:
2772:
2763:
2758:
2730:
2722:
2721:
2703:
2683:
2663:
2655:
2653:
2652:
2647:
2642:
2641:
2625:
2617:
2616:
2593:
2585:
2584:
2572:
2571:
2555:
2547:
2546:
2523:
2515:
2514:
2493:
2466:
2462:
2458:
2452:
2450:
2449:
2444:
2442:
2441:
2425:
2417:
2416:
2393:
2385:
2384:
2363:
2355:
2354:
2339:
2337:
2336:
2331:
2329:
2328:
2312:
2304:
2303:
2280:
2272:
2271:
2250:
2242:
2241:
2223:
2108:
2106:
2105:
2100:
2095:
2094:
2093:
2088:
2080:
2061:
2059:
2058:
2053:
2045:
2044:
2043:
2042:
2021:
2010:
1986:
1984:
1983:
1978:
1973:
1968:
1960:
1955:
1954:
1936:
1935:
1919:
1917:
1916:
1911:
1887:
1885:
1884:
1879:
1861:
1859:
1858:
1853:
1841:
1839:
1838:
1833:
1831:
1830:
1829:
1828:
1748:
1740:
1729:
1727:
1726:
1721:
1719:
1717:
1703:
1698:
1697:
1676:
1674:
1673:
1668:
1660:
1652:
1644:
1636:
1628:
1623:
1609:
1596:
1594:
1593:
1588:
1553:
1548:
1534:
1521:
1519:
1518:
1513:
1508:
1503:
1483:
1478:
1473:
1462:
1401:
1399:
1398:
1393:
1385:
1384:
1372:
1371:
1355:
1353:
1352:
1347:
1332:
1308:
1306:
1305:
1300:
1227:
1218:
1216:
1215:
1210:
1172:
1171:
1159:
1158:
1142:
1140:
1139:
1134:
1126:
1122:
1115:
1086:
1084:
1083:
1078:
1006:
995:
993:
992:
987:
982:
967:
965:
964:
959:
954:
950:
949:
941:
910:
906:
898:
877:
876:
864:
863:
847:
845:
844:
839:
834:
830:
825:
814:
802:
798:
793:
782:
732:
730:
729:
724:
644:
643:
631:
630:
606:
604:
603:
598:
586:
584:
583:
578:
522:
521:
501:
499:
498:
493:
465:
463:
462:
457:
452:
428:
426:
425:
420:
408:
406:
405:
400:
350:
349:
290:
282:
236:
134:phase difference
85:
78:
74:
71:
65:
45:
44:
37:
6951:
6950:
6946:
6945:
6944:
6942:
6941:
6940:
6921:
6920:
6919:
6914:
6896:
6882:Wigner's friend
6858:
6849:Quantum gravity
6810:
6796:Quantum sensing
6776:Quantum network
6756:Quantum machine
6726:Quantum imaging
6689:Quantum circuit
6684:Quantum channel
6643:
6589:Quantum biology
6575:
6551:Elitzur–Vaidman
6526:Davisson–Germer
6509:
6461:Hidden-variable
6451:de Broglie–Bohm
6428:Interpretations
6422:
6386:
6340:
6227:Complementarity
6205:
6162:
6157:
6124:Wayback Machine
6093:
6088:
6087:
6079:RS Longhurst,
6078:
6074:
6067:
6044:
6040:
6033:
6019:
6015:
5962:
5958:
5938:
5934:
5927:
5908:
5901:
5856:
5852:
5821:
5817:
5810:
5796:
5792:
5783:
5779:
5772:
5748:
5744:
5723:
5719:
5706:
5702:
5697:
5692:
5608:
5602:
5573:
5516:
5510:
5452:Richard Feynman
5438:
5432:
5427:
5362:
5356:
5351:
5310:
5306:
5304:
5301:
5300:
5268:
5264:
5262:
5259:
5258:
5231:
5228:
5227:
5210:
5205:
5204:
5183:
5179:
5174:
5165:
5160:
5159:
5138:
5134:
5129:
5127:
5124:
5123:
5087:
5082:
5057:
5053:
5029:
5025:
5004:
4999:
4993:
4990:
4989:
4969:
4966:
4965:
4949:
4946:
4945:
4929:
4926:
4925:
4893:
4889:
4865:
4861:
4838:
4835:
4834:
4802:
4798:
4796:
4793:
4792:
4760:
4756:
4754:
4751:
4750:
4713:
4708:
4683:
4679:
4655:
4651:
4630:
4625:
4609:
4604:
4603:
4582:
4578:
4573:
4564:
4559:
4558:
4537:
4533:
4528:
4519:
4514:
4513:
4490:
4473:
4470:
4469:
4437:
4433:
4409:
4405:
4382:
4379:
4378:
4320:
4316:
4307:
4302:
4301:
4278:
4261:
4258:
4257:
4241:
4238:
4237:
4212:
4209:
4208:
4166:
4163:
4162:
4153:– the observed
4144:
4115:
4114:
4113:
3878:
3870:
3869:
3815:
3814:Advanced topics
3807:
3806:
3805:
3757:Hidden-variable
3747:de Broglie–Bohm
3726:
3724:Interpretations
3716:
3715:
3714:
3684:
3676:
3675:
3674:
3632:
3624:
3623:
3622:
3589:
3545:CHSH inequality
3534:
3526:
3525:
3524:
3453:Complementarity
3447:
3439:
3438:
3437:
3405:
3376:
3351:
3340:
3339:
3325:
3315:
3310:
3302:
3299:
3298:
3281:
3271:
3264:
3261:
3252:
3249:
3240:
3237:
3184:
3146:
3121:
3094:
3085:
3081:
3070:
3061:
3057:
3038:
3029:
3025:
3017:
3008:
3004:
3002:
2988:
2979:
2975:
2964:
2955:
2951:
2940:
2932:
2929:
2928:
2899:
2890:
2886:
2875:
2866:
2862:
2845:
2836:
2832:
2824:
2815:
2811:
2797:
2788:
2783:
2768:
2759:
2754:
2726:
2717:
2713:
2699:
2679:
2671:
2668:
2667:
2659:
2621:
2612:
2608:
2601:
2597:
2589:
2580:
2576:
2551:
2542:
2538:
2531:
2527:
2519:
2510:
2506:
2489:
2481:
2478:
2477:
2467:represents the
2464:
2460:
2456:
2421:
2412:
2408:
2401:
2397:
2389:
2380:
2376:
2359:
2350:
2346:
2344:
2341:
2340:
2308:
2299:
2295:
2288:
2284:
2276:
2267:
2263:
2246:
2237:
2233:
2231:
2228:
2227:
2219:
2182:
2132:
2081:
2079:
2075:
2071:
2069:
2066:
2065:
2038:
2034:
2030:
2026:
2011:
2000:
1994:
1991:
1990:
1961:
1959:
1944:
1940:
1931:
1927:
1925:
1922:
1921:
1893:
1890:
1889:
1867:
1864:
1863:
1847:
1844:
1843:
1824:
1820:
1816:
1812:
1807:
1804:
1803:
1782:
1758:
1746:
1738:
1733:
1707:
1702:
1693:
1689:
1687:
1684:
1683:
1651:
1635:
1610:
1608:
1606:
1603:
1602:
1535:
1533:
1531:
1528:
1527:
1484:
1482:
1463:
1461:
1450:
1447:
1446:
1408:
1380:
1376:
1367:
1363:
1361:
1358:
1357:
1328:
1314:
1311:
1310:
1233:
1230:
1229:
1225:
1167:
1163:
1154:
1150:
1148:
1145:
1144:
1111:
1098:
1094:
1092:
1089:
1088:
1012:
1009:
1008:
1004:
978:
973:
970:
969:
940:
921:
917:
897:
893:
872:
868:
859:
855:
853:
850:
849:
815:
813:
809:
783:
781:
777:
742:
739:
738:
639:
635:
626:
622:
620:
617:
616:
592:
589:
588:
517:
513:
511:
508:
507:
475:
472:
471:
448:
434:
431:
430:
414:
411:
410:
345:
341:
339:
336:
335:
328:
313:interferometers
288:
280:
225:
207:
179:
86:
75:
69:
66:
58:help improve it
55:
46:
42:
35:
24:
17:
12:
11:
5:
6949:
6939:
6938:
6936:Wave mechanics
6933:
6916:
6915:
6913:
6912:
6901:
6898:
6897:
6895:
6894:
6889:
6884:
6879:
6878:
6877:
6866:
6864:
6860:
6859:
6857:
6856:
6851:
6846:
6845:
6844:
6834:
6829:
6827:Casimir effect
6824:
6818:
6816:
6812:
6811:
6809:
6808:
6803:
6798:
6793:
6788:
6786:Quantum optics
6783:
6778:
6773:
6768:
6763:
6758:
6753:
6748:
6743:
6738:
6733:
6728:
6723:
6718:
6713:
6708:
6707:
6706:
6696:
6691:
6686:
6681:
6680:
6679:
6669:
6664:
6659:
6653:
6651:
6645:
6644:
6642:
6641:
6636:
6631:
6626:
6621:
6616:
6611:
6606:
6601:
6596:
6591:
6585:
6583:
6577:
6576:
6574:
6573:
6568:
6563:
6561:Quantum eraser
6558:
6553:
6548:
6543:
6538:
6533:
6528:
6523:
6517:
6515:
6511:
6510:
6508:
6507:
6502:
6497:
6492:
6487:
6482:
6477:
6476:
6475:
6474:
6473:
6458:
6453:
6448:
6443:
6438:
6432:
6430:
6424:
6423:
6421:
6420:
6415:
6410:
6405:
6400:
6394:
6392:
6388:
6387:
6385:
6384:
6379:
6374:
6369:
6364:
6359:
6354:
6348:
6346:
6342:
6341:
6339:
6338:
6337:
6336:
6331:
6321:
6316:
6311:
6306:
6301:
6296:
6291:
6286:
6281:
6276:
6271:
6266:
6261:
6260:
6259:
6254:
6249:
6244:
6234:
6232:Density matrix
6229:
6224:
6219:
6213:
6211:
6207:
6206:
6204:
6203:
6198:
6193:
6188:
6187:
6186:
6176:
6170:
6168:
6164:
6163:
6156:
6155:
6148:
6141:
6133:
6127:
6126:
6114:
6109:
6104:
6099:
6092:
6091:External links
6089:
6086:
6085:
6072:
6065:
6038:
6032:978-0525949695
6031:
6013:
5956:
5932:
5925:
5899:
5864:Optics Express
5850:
5815:
5808:
5800:Interferometry
5790:
5786:Phase contrast
5777:
5770:
5742:
5717:
5699:
5698:
5696:
5693:
5691:
5690:
5685:
5680:
5675:
5670:
5668:Newton's rings
5665:
5660:
5655:
5653:Lloyd's Mirror
5650:
5648:Interferometer
5645:
5640:
5635:
5630:
5625:
5620:
5615:
5609:
5607:
5604:
5595:. A vibrating
5587:, wavelength,
5572:
5569:
5512:Main article:
5509:
5506:
5434:Main article:
5431:
5428:
5425:Interferometry
5423:Main article:
5358:Main article:
5355:
5352:
5350:
5347:
5330:
5327:
5324:
5321:
5318:
5313:
5309:
5288:
5285:
5282:
5279:
5276:
5271:
5267:
5235:
5213:
5208:
5203:
5200:
5197:
5194:
5191:
5186:
5182:
5177:
5173:
5168:
5163:
5158:
5155:
5152:
5149:
5146:
5141:
5137:
5132:
5107:
5104:
5101:
5098:
5095:
5090:
5085:
5081:
5077:
5074:
5071:
5068:
5065:
5060:
5056:
5052:
5049:
5046:
5043:
5040:
5037:
5032:
5028:
5024:
5021:
5018:
5015:
5012:
5007:
5002:
4998:
4973:
4953:
4933:
4913:
4910:
4907:
4904:
4901:
4896:
4892:
4888:
4885:
4882:
4879:
4876:
4873:
4868:
4864:
4860:
4857:
4854:
4851:
4848:
4845:
4842:
4822:
4819:
4816:
4813:
4810:
4805:
4801:
4780:
4777:
4774:
4771:
4768:
4763:
4759:
4736:
4733:
4730:
4727:
4724:
4721:
4716:
4711:
4707:
4703:
4700:
4697:
4694:
4691:
4686:
4682:
4678:
4675:
4672:
4669:
4666:
4663:
4658:
4654:
4650:
4647:
4644:
4641:
4638:
4633:
4628:
4624:
4620:
4617:
4612:
4607:
4602:
4599:
4596:
4593:
4590:
4585:
4581:
4576:
4572:
4567:
4562:
4557:
4554:
4551:
4548:
4545:
4540:
4536:
4531:
4527:
4522:
4517:
4512:
4509:
4506:
4503:
4500:
4497:
4493:
4489:
4486:
4483:
4480:
4477:
4457:
4454:
4451:
4448:
4445:
4440:
4436:
4432:
4429:
4426:
4423:
4420:
4417:
4412:
4408:
4404:
4401:
4398:
4395:
4392:
4389:
4386:
4358:
4355:
4352:
4349:
4346:
4343:
4340:
4337:
4334:
4331:
4328:
4323:
4319:
4315:
4310:
4305:
4300:
4297:
4294:
4291:
4288:
4285:
4281:
4277:
4274:
4271:
4268:
4265:
4245:
4225:
4222:
4219:
4216:
4185:
4182:
4179:
4176:
4173:
4170:
4146:
4145:
4143:
4142:
4135:
4128:
4120:
4117:
4116:
4112:
4111:
4106:
4101:
4096:
4091:
4086:
4081:
4076:
4071:
4066:
4061:
4056:
4051:
4046:
4041:
4036:
4031:
4026:
4021:
4016:
4011:
4006:
4001:
3996:
3991:
3986:
3981:
3976:
3971:
3966:
3961:
3956:
3951:
3946:
3941:
3936:
3931:
3926:
3921:
3916:
3911:
3906:
3901:
3896:
3891:
3886:
3880:
3879:
3876:
3875:
3872:
3871:
3868:
3867:
3862:
3857:
3852:
3850:Density matrix
3847:
3842:
3837:
3832:
3827:
3822:
3816:
3813:
3812:
3809:
3808:
3804:
3803:
3798:
3793:
3788:
3783:
3778:
3773:
3772:
3771:
3770:
3769:
3754:
3749:
3744:
3739:
3734:
3728:
3727:
3722:
3721:
3718:
3717:
3713:
3712:
3707:
3702:
3697:
3692:
3686:
3685:
3682:
3681:
3678:
3677:
3673:
3672:
3667:
3662:
3657:
3652:
3647:
3641:
3640:
3639:
3633:
3630:
3629:
3626:
3625:
3621:
3620:
3615:
3610:
3604:
3603:
3602:
3601:
3600:
3598:Delayed-choice
3593:Quantum eraser
3588:
3587:
3582:
3577:
3572:
3567:
3562:
3557:
3552:
3547:
3542:
3536:
3535:
3532:
3531:
3528:
3527:
3523:
3522:
3521:
3520:
3510:
3505:
3500:
3495:
3490:
3485:
3483:Quantum number
3480:
3475:
3470:
3465:
3460:
3455:
3449:
3448:
3445:
3444:
3441:
3440:
3436:
3435:
3430:
3424:
3423:
3422:
3417:
3412:
3406:
3403:
3402:
3399:
3398:
3397:
3396:
3391:
3386:
3378:
3377:
3372:
3361:
3358:
3354:
3347:
3344:
3338:
3335:
3332:
3328:
3321:
3318:
3314:
3309:
3306:
3295:
3294:
3288:
3287:
3270:
3267:
3266:
3265:
3262:
3255:
3253:
3250:
3243:
3241:
3238:
3231:
3229:
3211:Lloyd's mirror
3183:
3180:
3145:
3142:
3107:
3104:
3101:
3097:
3093:
3088:
3084:
3080:
3077:
3073:
3069:
3064:
3060:
3056:
3053:
3050:
3045:
3041:
3037:
3032:
3028:
3024:
3020:
3016:
3011:
3007:
3001:
2998:
2995:
2991:
2987:
2982:
2978:
2974:
2971:
2967:
2963:
2958:
2954:
2950:
2947:
2943:
2939:
2936:
2912:
2909:
2906:
2902:
2898:
2893:
2889:
2885:
2882:
2878:
2874:
2869:
2865:
2861:
2858:
2855:
2852:
2848:
2844:
2839:
2835:
2831:
2827:
2823:
2818:
2814:
2810:
2807:
2804:
2800:
2796:
2791:
2786:
2782:
2778:
2775:
2771:
2767:
2762:
2757:
2753:
2749:
2746:
2743:
2739:
2736:
2733:
2729:
2725:
2720:
2716:
2712:
2709:
2706:
2702:
2698:
2695:
2692:
2689:
2686:
2682:
2678:
2675:
2645:
2640:
2637:
2634:
2631:
2628:
2624:
2620:
2615:
2611:
2607:
2604:
2600:
2596:
2592:
2588:
2583:
2579:
2575:
2570:
2567:
2564:
2561:
2558:
2554:
2550:
2545:
2541:
2537:
2534:
2530:
2526:
2522:
2518:
2513:
2509:
2505:
2502:
2499:
2496:
2492:
2488:
2485:
2440:
2437:
2434:
2431:
2428:
2424:
2420:
2415:
2411:
2407:
2404:
2400:
2396:
2392:
2388:
2383:
2379:
2375:
2372:
2369:
2366:
2362:
2358:
2353:
2349:
2327:
2324:
2321:
2318:
2315:
2311:
2307:
2302:
2298:
2294:
2291:
2287:
2283:
2279:
2275:
2270:
2266:
2262:
2259:
2256:
2253:
2249:
2245:
2240:
2236:
2181:
2178:
2177:
2176:
2173:
2166:
2151:wave functions
2131:
2128:
2098:
2091:
2087:
2084:
2078:
2074:
2051:
2048:
2041:
2037:
2033:
2029:
2025:
2020:
2017:
2014:
2009:
2006:
2003:
1999:
1976:
1971:
1967:
1964:
1958:
1953:
1950:
1947:
1943:
1939:
1934:
1930:
1909:
1906:
1903:
1900:
1897:
1877:
1874:
1871:
1851:
1827:
1823:
1819:
1815:
1811:
1781:
1780:Multiple beams
1778:
1757:
1754:
1736:
1716:
1713:
1710:
1706:
1701:
1696:
1692:
1666:
1663:
1658:
1655:
1650:
1647:
1642:
1639:
1634:
1631:
1626:
1622:
1619:
1616:
1613:
1586:
1583:
1580:
1577:
1574:
1571:
1568:
1565:
1562:
1559:
1556:
1551:
1547:
1544:
1541:
1538:
1511:
1506:
1502:
1499:
1496:
1493:
1490:
1487:
1481:
1476:
1472:
1469:
1466:
1460:
1457:
1454:
1407:
1404:
1403:
1402:
1391:
1388:
1383:
1379:
1375:
1370:
1366:
1344:
1341:
1338:
1335:
1331:
1327:
1324:
1321:
1318:
1298:
1295:
1292:
1289:
1285:
1282:
1279:
1275:
1272:
1268:
1265:
1262:
1258:
1255:
1252:
1249:
1246:
1243:
1240:
1237:
1219:
1208:
1205:
1202:
1199:
1196:
1193:
1190:
1187:
1184:
1181:
1178:
1175:
1170:
1166:
1162:
1157:
1153:
1132:
1129:
1125:
1121:
1118:
1114:
1110:
1107:
1104:
1101:
1097:
1076:
1073:
1070:
1067:
1064:
1061:
1058:
1055:
1052:
1049:
1046:
1043:
1040:
1037:
1034:
1031:
1028:
1025:
1022:
1019:
1016:
985:
981:
977:
957:
953:
947:
944:
939:
936:
933:
930:
927:
924:
920:
916:
913:
909:
904:
901:
896:
892:
889:
886:
883:
880:
875:
871:
867:
862:
858:
837:
833:
828:
824:
821:
818:
812:
808:
805:
801:
796:
792:
789:
786:
780:
776:
773:
770:
767:
764:
761:
758:
755:
752:
749:
746:
722:
719:
716:
713:
710:
707:
704:
701:
698:
695:
692:
689:
686:
683:
680:
677:
674:
671:
668:
665:
662:
659:
656:
653:
650:
647:
642:
638:
634:
629:
625:
596:
576:
573:
570:
567:
564:
561:
558:
555:
552:
549:
546:
543:
540:
537:
534:
531:
528:
525:
520:
516:
491:
488:
485:
482:
479:
455:
451:
447:
444:
441:
438:
418:
398:
395:
392:
389:
386:
383:
380:
377:
374:
371:
368:
365:
362:
359:
356:
353:
348:
344:
327:
324:
206:
203:
178:
175:
88:
87:
49:
47:
40:
15:
9:
6:
4:
3:
2:
6948:
6937:
6934:
6932:
6929:
6928:
6926:
6911:
6903:
6902:
6899:
6893:
6890:
6888:
6885:
6883:
6880:
6876:
6873:
6872:
6871:
6868:
6867:
6865:
6861:
6855:
6852:
6850:
6847:
6843:
6840:
6839:
6838:
6835:
6833:
6830:
6828:
6825:
6823:
6820:
6819:
6817:
6813:
6807:
6804:
6802:
6799:
6797:
6794:
6792:
6789:
6787:
6784:
6782:
6779:
6777:
6774:
6772:
6769:
6767:
6764:
6762:
6759:
6757:
6754:
6752:
6749:
6747:
6746:Quantum logic
6744:
6742:
6739:
6737:
6734:
6732:
6729:
6727:
6724:
6722:
6719:
6717:
6714:
6712:
6709:
6705:
6702:
6701:
6700:
6697:
6695:
6692:
6690:
6687:
6685:
6682:
6678:
6675:
6674:
6673:
6670:
6668:
6665:
6663:
6660:
6658:
6655:
6654:
6652:
6650:
6646:
6640:
6637:
6635:
6632:
6630:
6627:
6625:
6622:
6620:
6617:
6615:
6612:
6610:
6607:
6605:
6602:
6600:
6599:Quantum chaos
6597:
6595:
6592:
6590:
6587:
6586:
6584:
6582:
6578:
6572:
6569:
6567:
6566:Stern–Gerlach
6564:
6562:
6559:
6557:
6554:
6552:
6549:
6547:
6544:
6542:
6539:
6537:
6534:
6532:
6529:
6527:
6524:
6522:
6519:
6518:
6516:
6512:
6506:
6503:
6501:
6500:Transactional
6498:
6496:
6493:
6491:
6490:Quantum logic
6488:
6486:
6483:
6481:
6478:
6472:
6469:
6468:
6467:
6464:
6463:
6462:
6459:
6457:
6454:
6452:
6449:
6447:
6444:
6442:
6439:
6437:
6434:
6433:
6431:
6429:
6425:
6419:
6416:
6414:
6411:
6409:
6406:
6404:
6401:
6399:
6396:
6395:
6393:
6389:
6383:
6380:
6378:
6375:
6373:
6370:
6368:
6365:
6363:
6360:
6358:
6355:
6353:
6350:
6349:
6347:
6343:
6335:
6332:
6330:
6327:
6326:
6325:
6324:Wave function
6322:
6320:
6317:
6315:
6312:
6310:
6307:
6305:
6302:
6300:
6299:Superposition
6297:
6295:
6294:Quantum state
6292:
6290:
6287:
6285:
6282:
6280:
6277:
6275:
6272:
6270:
6267:
6265:
6262:
6258:
6255:
6253:
6250:
6248:
6247:Excited state
6245:
6243:
6240:
6239:
6238:
6235:
6233:
6230:
6228:
6225:
6223:
6220:
6218:
6215:
6214:
6212:
6208:
6202:
6199:
6197:
6194:
6192:
6189:
6185:
6182:
6181:
6180:
6177:
6175:
6172:
6171:
6169:
6165:
6161:
6154:
6149:
6147:
6142:
6140:
6135:
6134:
6131:
6125:
6121:
6118:
6115:
6113:
6110:
6108:
6105:
6103:
6100:
6098:
6095:
6094:
6082:
6076:
6068:
6062:
6058:
6054:
6053:
6048:
6047:Greene, Brian
6042:
6034:
6028:
6024:
6017:
6009:
6005:
6001:
5997:
5993:
5989:
5984:
5979:
5975:
5971:
5967:
5960:
5953:
5949:
5945:
5941:
5936:
5928:
5926:0-521-64222-1
5922:
5918:
5917:
5912:
5906:
5904:
5895:
5891:
5886:
5881:
5877:
5873:
5869:
5865:
5861:
5854:
5846:
5842:
5838:
5834:
5830:
5826:
5819:
5811:
5809:0-521-31162-4
5805:
5801:
5794:
5787:
5781:
5773:
5767:
5763:
5759:
5755:
5754:
5746:
5738:
5734:
5730:
5729:
5721:
5713:
5712:
5704:
5700:
5689:
5686:
5684:
5681:
5679:
5676:
5674:
5671:
5669:
5666:
5664:
5661:
5659:
5658:Moiré pattern
5656:
5654:
5651:
5649:
5646:
5644:
5641:
5639:
5636:
5634:
5631:
5629:
5626:
5624:
5621:
5619:
5616:
5614:
5611:
5610:
5603:
5600:
5598:
5594:
5590:
5586:
5582:
5578:
5568:
5566:
5562:
5558:
5557:optical fiber
5554:
5550:
5549:coaxial cable
5545:
5537:
5533:
5529:
5525:
5520:
5515:
5505:
5503:
5499:
5494:
5492:
5487:
5483:
5479:
5475:
5470:
5468:
5464:
5460:
5455:
5453:
5449:
5445:
5441:
5437:
5426:
5421:
5419:
5415:
5410:
5406:
5402:
5397:
5395:
5391:
5387:
5383:
5379:
5375:
5371:
5367:
5361:
5346:
5344:
5325:
5322:
5319:
5311:
5283:
5280:
5277:
5269:
5256:
5252:
5247:
5233:
5211:
5198:
5195:
5192:
5184:
5171:
5166:
5153:
5150:
5147:
5139:
5121:
5102:
5099:
5096:
5088:
5083:
5072:
5069:
5066:
5058:
5050:
5044:
5041:
5038:
5030:
5019:
5016:
5013:
5005:
5000:
4987:
4971:
4951:
4931:
4908:
4905:
4902:
4894:
4886:
4880:
4877:
4874:
4866:
4858:
4852:
4849:
4846:
4817:
4814:
4811:
4803:
4775:
4772:
4769:
4761:
4747:
4728:
4725:
4722:
4714:
4709:
4698:
4695:
4692:
4684:
4676:
4670:
4667:
4664:
4656:
4645:
4642:
4639:
4631:
4626:
4615:
4610:
4597:
4594:
4591:
4583:
4570:
4565:
4552:
4549:
4546:
4538:
4525:
4520:
4507:
4504:
4501:
4487:
4481:
4475:
4452:
4449:
4446:
4438:
4430:
4424:
4421:
4418:
4410:
4402:
4396:
4393:
4390:
4377:of two terms
4376:
4372:
4353:
4350:
4347:
4335:
4332:
4329:
4321:
4313:
4308:
4295:
4292:
4289:
4275:
4269:
4263:
4243:
4220:
4214:
4207:
4203:
4199:
4180:
4177:
4174:
4160:
4156:
4152:
4141:
4136:
4134:
4129:
4127:
4122:
4121:
4119:
4118:
4110:
4107:
4105:
4102:
4100:
4097:
4095:
4092:
4090:
4087:
4085:
4082:
4080:
4077:
4075:
4072:
4070:
4067:
4065:
4062:
4060:
4057:
4055:
4052:
4050:
4047:
4045:
4042:
4040:
4037:
4035:
4032:
4030:
4027:
4025:
4022:
4020:
4017:
4015:
4012:
4010:
4007:
4005:
4002:
4000:
3997:
3995:
3992:
3990:
3987:
3985:
3982:
3980:
3977:
3975:
3972:
3970:
3967:
3965:
3962:
3960:
3957:
3955:
3952:
3950:
3947:
3945:
3942:
3940:
3937:
3935:
3932:
3930:
3927:
3925:
3922:
3920:
3917:
3915:
3912:
3910:
3907:
3905:
3902:
3900:
3897:
3895:
3892:
3890:
3887:
3885:
3882:
3881:
3874:
3873:
3866:
3863:
3861:
3858:
3856:
3853:
3851:
3848:
3846:
3843:
3841:
3840:Quantum chaos
3838:
3836:
3833:
3831:
3828:
3826:
3823:
3821:
3818:
3817:
3811:
3810:
3802:
3799:
3797:
3796:Transactional
3794:
3792:
3789:
3787:
3786:Quantum logic
3784:
3782:
3779:
3777:
3774:
3768:
3765:
3764:
3763:
3760:
3759:
3758:
3755:
3753:
3750:
3748:
3745:
3743:
3740:
3738:
3735:
3733:
3730:
3729:
3725:
3720:
3719:
3711:
3708:
3706:
3703:
3701:
3698:
3696:
3693:
3691:
3688:
3687:
3680:
3679:
3671:
3668:
3666:
3663:
3661:
3658:
3656:
3653:
3651:
3648:
3646:
3643:
3642:
3638:
3635:
3634:
3628:
3627:
3619:
3616:
3614:
3611:
3609:
3606:
3605:
3599:
3596:
3595:
3594:
3591:
3590:
3586:
3583:
3581:
3578:
3576:
3573:
3571:
3568:
3566:
3563:
3561:
3558:
3556:
3553:
3551:
3548:
3546:
3543:
3541:
3538:
3537:
3530:
3529:
3519:
3516:
3515:
3514:
3513:Wave function
3511:
3509:
3506:
3504:
3501:
3499:
3496:
3494:
3493:Superposition
3491:
3489:
3486:
3484:
3481:
3479:
3476:
3474:
3471:
3469:
3466:
3464:
3461:
3459:
3456:
3454:
3451:
3450:
3443:
3442:
3434:
3431:
3429:
3426:
3425:
3421:
3418:
3416:
3413:
3411:
3408:
3407:
3401:
3400:
3395:
3392:
3390:
3387:
3385:
3382:
3381:
3380:
3379:
3375:
3342:
3336:
3319:
3316:
3312:
3304:
3297:
3296:
3293:
3290:
3289:
3285:
3284:
3280:
3276:
3259:
3254:
3247:
3242:
3235:
3230:
3227:
3226:
3225:
3223:
3219:
3214:
3212:
3208:
3203:
3201:
3197:
3193:
3192:beam splitter
3188:
3179:
3175:
3171:
3168:
3163:
3160:
3156:
3150:
3141:
3137:
3135:
3130:
3125:
3118:
3105:
3086:
3082:
3078:
3062:
3058:
3051:
3048:
3030:
3026:
3009:
3005:
2999:
2996:
2980:
2976:
2972:
2956:
2952:
2948:
2934:
2926:
2923:
2910:
2891:
2887:
2883:
2867:
2863:
2856:
2853:
2837:
2833:
2816:
2812:
2808:
2805:
2789:
2784:
2780:
2776:
2760:
2755:
2751:
2747:
2744:
2741:
2734:
2731:
2718:
2714:
2707:
2704:
2693:
2690:
2687:
2673:
2665:
2662:
2656:
2643:
2635:
2632:
2629:
2613:
2609:
2602:
2598:
2581:
2577:
2573:
2565:
2562:
2559:
2543:
2539:
2532:
2528:
2511:
2507:
2503:
2497:
2494:
2483:
2475:
2472:
2470:
2453:
2435:
2432:
2429:
2413:
2409:
2402:
2398:
2381:
2377:
2373:
2367:
2364:
2351:
2347:
2322:
2319:
2316:
2300:
2296:
2289:
2285:
2268:
2264:
2260:
2254:
2251:
2238:
2234:
2225:
2222:
2216:
2208:
2204:
2203:
2198:
2197:
2191:
2186:
2174:
2171:
2167:
2164:
2160:
2156:
2154:
2152:
2148:
2144:
2140:
2139:gravity waves
2136:
2127:
2125:
2121:
2116:
2114:
2109:
2096:
2089:
2085:
2082:
2076:
2072:
2062:
2049:
2046:
2039:
2035:
2031:
2027:
2023:
2018:
2015:
2012:
2007:
2004:
2001:
1997:
1989:To show that
1987:
1974:
1969:
1965:
1962:
1956:
1951:
1948:
1945:
1941:
1937:
1932:
1928:
1907:
1904:
1901:
1898:
1895:
1875:
1872:
1869:
1849:
1825:
1821:
1817:
1813:
1809:
1801:
1796:
1794:
1790:
1789:3-phase power
1785:
1777:
1774:
1771:
1762:
1753:
1750:
1744:
1739:
1730:
1714:
1711:
1708:
1704:
1699:
1694:
1690:
1681:
1677:
1664:
1661:
1656:
1653:
1648:
1645:
1640:
1637:
1632:
1629:
1624:
1620:
1617:
1614:
1611:
1600:
1597:
1584:
1581:
1578:
1575:
1572:
1569:
1566:
1563:
1560:
1557:
1554:
1549:
1545:
1542:
1539:
1536:
1525:
1522:
1509:
1504:
1500:
1497:
1494:
1491:
1488:
1485:
1479:
1474:
1470:
1467:
1464:
1458:
1455:
1444:
1442:
1438:
1434:
1429:
1420:
1412:
1389:
1386:
1381:
1377:
1373:
1368:
1364:
1342:
1339:
1333:
1329:
1325:
1319:
1316:
1296:
1293:
1290:
1287:
1283:
1280:
1277:
1273:
1270:
1266:
1263:
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681:
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669:
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375:
372:
369:
366:
360:
357:
354:
346:
342:
333:
323:
321:
316:
314:
310:
306:
305:laser speckle
302:
296:
292:
286:
278:
277:even multiple
274:
264:
260:
257:
253:
249:
245:
219:
211:
202:
200:
196:
192:
188:
184:
174:
172:
168:
167:gravity waves
164:
160:
156:
152:
148:
147:
142:
141:
136:
135:
130:
127:
123:
119:
111:
107:
103:
99:
94:
84:
81:
73:
70:February 2022
63:
59:
53:
50:This article
48:
39:
38:
33:
29:
28:Moiré pattern
22:
6931:Interference
6629:Quantum mind
6541:Franck–Hertz
6403:Klein–Gordon
6352:Formulations
6345:Formulations
6274:Interference
6273:
6264:Entanglement
6242:Ground state
6237:Energy level
6210:Fundamentals
6174:Introduction
6080:
6075:
6051:
6041:
6022:
6016:
5973:
5969:
5959:
5935:
5914:
5867:
5863:
5853:
5828:
5824:
5818:
5799:
5793:
5780:
5752:
5745:
5727:
5720:
5710:
5703:
5601:
5574:
5541:
5495:
5471:
5456:
5444:Thomas Young
5442:
5439:
5398:
5385:
5374:interference
5369:
5363:
5349:Applications
5255:matter waves
5248:
4985:
4748:
4198:wavefunction
4157:– resembles
4150:
4149:
3695:Klein–Gordon
3631:Formulations
3468:Energy level
3463:Entanglement
3446:Fundamentals
3433:Interference
3432:
3384:Introduction
3251:An oil spill
3215:
3204:
3189:
3185:
3176:
3172:
3164:
3151:
3147:
3138:
3129:polarization
3126:
3119:
2927:
2924:
2666:
2664:is given by
2660:
2657:
2476:
2473:
2454:
2226:
2220:
2212:
2206:
2201:
2200:
2195:
2194:
2190:optical flat
2147:matter waves
2133:
2117:
2110:
2063:
1988:
1797:
1786:
1783:
1775:
1770:point source
1767:
1751:
1734:
1731:
1682:
1678:
1601:
1598:
1526:
1523:
1445:
1443:is given by
1440:
1436:
1432:
1425:
1221:
1000:
329:
320:matter waves
317:
297:
293:
285:odd multiple
284:
276:
270:
241:
199:Thomas Young
194:
190:
183:interference
182:
180:
171:matter waves
145:
144:
139:
138:
132:
122:interference
121:
115:
109:
106:Out of phase
101:
76:
67:
51:
6887:EPR paradox
6667:Quantum bus
6536:Double-slit
6514:Experiments
6480:Many-worlds
6418:Schrödinger
6382:Phase space
6372:Schrödinger
6362:Interaction
6319:Uncertainty
6289:Nonlocality
6284:Measurement
6279:Decoherence
6269:Hamiltonian
5628:Diffraction
5498:slip gauges
5491:calibration
5382:frequencies
5343:matter wave
4206:probability
4084:von Neumann
4069:Schrödinger
3845:EPR paradox
3776:Many-worlds
3710:Schrödinger
3665:Schrödinger
3660:Phase-space
3650:Interaction
3555:Double-slit
3533:Experiments
3508:Uncertainty
3478:Nonlocality
3473:Measurement
3458:Decoherence
3428:Hamiltonian
3279:Matter wave
3218:iridescence
2209:, are seen.
1862:waves from
1428:plane waves
6925:Categories
6815:Extensions
6649:Technology
6495:Relational
6446:Copenhagen
6357:Heisenberg
6304:Tunnelling
6167:Background
5944:Leighton R
5695:References
5589:absorption
5532:telescopes
5394:difference
4079:Sommerfeld
3994:Heisenberg
3989:Gutzwiller
3929:de Broglie
3877:Scientists
3791:Relational
3742:Copenhagen
3645:Heisenberg
3503:Tunnelling
3404:Background
3273:See also:
3167:laser beam
2135:Mechanical
1743:wavelength
733:Using the
468:wavenumber
332:sinusoidal
267:thickness.
252:vector sum
205:Mechanisms
6521:Bell test
6391:Equations
6217:Born rule
6000:1367-2630
5983:1210.6243
5940:Feynman R
5911:Born, Max
5825:Phys. Rev
5593:impedance
5553:waveguide
5478:Michelson
5386:perceived
5366:acoustics
5308:Ψ
5266:Ψ
5181:Ψ
5136:Ψ
5089:∗
5080:Ψ
5055:Ψ
5027:Ψ
5006:∗
4997:Ψ
4891:Ψ
4863:Ψ
4841:Ψ
4800:Ψ
4758:Ψ
4749:Usually,
4715:∗
4706:Ψ
4681:Ψ
4653:Ψ
4632:∗
4623:Ψ
4580:Ψ
4535:Ψ
4496:Ψ
4435:Ψ
4407:Ψ
4385:Ψ
4342:Ψ
4322:∗
4318:Ψ
4284:Ψ
4169:Ψ
4109:Zeilinger
3954:Ehrenfest
3683:Equations
3360:⟩
3357:Ψ
3346:^
3334:⟩
3331:Ψ
3308:ℏ
3083:φ
3079:−
3059:φ
3052:
2888:φ
2884:−
2864:φ
2857:
2748:∝
2719:∗
2691:∫
2633:ω
2630:−
2610:φ
2563:ω
2560:−
2540:φ
2433:ω
2430:−
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2320:ω
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2297:φ
2215:intensity
2086:π
2036:φ
2016:−
1998:∑
1966:π
1949:−
1942:φ
1938:−
1929:φ
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1705:λ
1665:…
1649:±
1633:±
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1564:±
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1498:
1489:π
1475:λ
1468:π
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1453:Δ
1326:φ
1320:
1297:…
1291:π
1281:π
1271:π
1264:π
1261:−
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1109:φ
1103:
1075:…
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1060:π
1045:π
1039:−
1033:π
1027:−
1021:…
1015:φ
976:φ
943:φ
932:ω
929:−
915:
900:φ
891:
807:
788:−
775:
760:
748:
712:φ
703:ω
700:−
688:
673:ω
670:−
658:
613:superpose
595:φ
572:φ
563:ω
560:−
548:
487:π
478:ω
454:λ
446:π
391:ω
388:−
376:
248:amplitude
201:in 1801.
181:The word
177:Etymology
6910:Category
6704:Timeline
6456:Ensemble
6436:Bayesian
6329:Collapse
6201:Glossary
6184:Timeline
6120:Archived
6049:(1999).
5948:Sands M.
5894:25401860
5606:See also
5585:velocity
4034:Millikan
3959:Einstein
3944:Davisson
3899:Blackett
3884:Aharonov
3752:Ensemble
3732:Bayesian
3637:Overview
3518:Collapse
3498:Symmetry
3389:Glossary
3198:and the
2170:coherent
1920:, where
1791:and the
159:acoustic
126:coherent
98:In phase
6863:Related
6842:History
6581:Science
6413:Rydberg
6179:History
5872:Bibcode
5833:Bibcode
5597:crystal
5482:cadmium
5409:tremolo
4074:Simmons
4064:Rydberg
4029:Moseley
4009:Kramers
3999:Hilbert
3984:Glauber
3979:Feynman
3964:Everett
3934:Compton
3705:Rydberg
3394:History
3155:sodium-
2163:complex
2143:optical
1800:phasors
609:radians
502:is the
466:is the
118:physics
56:Please
6556:Popper
6063:
6057:97–109
6029:
6008:832961
6006:
5998:
5946:, and
5923:
5892:
5806:
5768:
5688:Upfade
5405:unison
5401:tuning
5390:volume
5378:sounds
5372:is an
4161:. Let
4104:Zeeman
4099:Wigner
4049:Planck
4019:Landau
4004:Jordan
3655:Matrix
3585:Popper
2455:where
587:where
409:where
189:words
6466:Local
6408:Pauli
6398:Dirac
6004:S2CID
5978:arXiv
5591:, or
5526:, an
5399:With
4988:, is
4196:be a
4059:Raman
4044:Pauli
4039:Onnes
3974:Fermi
3949:Debye
3939:Dirac
3904:Bloch
3894:Bethe
3762:Local
3700:Pauli
3690:Dirac
3488:State
1309:then
1087:then
273:phase
256:crest
191:inter
187:Latin
169:, or
155:radio
151:light
129:waves
6061:ISBN
6027:ISBN
5996:ISSN
5921:ISBN
5890:PMID
5804:ISBN
5766:ISBN
5522:The
5370:beat
5368:, a
5354:Beat
4791:and
4094:Wien
4089:Weyl
4054:Rabi
4024:Laue
4014:Lamb
3969:Fock
3924:Bose
3919:Born
3914:Bohr
3909:Bohm
3889:Bell
3277:and
3220:and
3209:and
2224:is:
2159:real
2145:and
2137:and
2111:The
1842:for
1732:and
470:and
311:and
242:The
195:fere
5988:doi
5880:doi
5841:doi
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1100:cos
912:cos
888:cos
804:cos
772:cos
757:cos
745:cos
685:cos
655:cos
545:cos
373:cos
315:.
287:of
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116:In
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