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Encyclopedia > Interference Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). Absolute value snapshots of the (real-valued, scalar) wave field. As time progresses, the wave fronts would move outwards from the two centers, but the dark regions (destructive interference) stay fixed.

Interference is the addition (superposition) of two or more waves that result in a new wave pattern. Interference may refer to : the physical phenomenon of wave interference, see interference the legal concept of humanitarian interference the interference proceeding of the U.S. patent law interference in baseball the chess tactic of interference of the enemys defence the communications concept where interference is anything which alters, modifies... Interference of two circular waves, snapshots of absolute value of (real,scalar) wave field for different wave lengths and distances of point sources File links The following pages link to this file: Interference Categories: GFDL images ... In linear algebra, the principle of superposition states that, for a linear system, a linear combination of solutions to the system is also a solution to the same linear system. ... Surface waves in water This article is about waves in the most general scientific sense. ...

As most commonly used, the term interference usually refers to the interaction of waves which are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Coherence is the property of wave-like states that enables them to exhibit interference. ... For other uses, see Frequency (disambiguation). ...

Two non-monochromatic waves are only fully coherent with each other if they both have exactly the same range of wavelengths and the same phase differences at each of the constituent wavelengths. Something which is monochromatic has a single color. ... Coherence is from Latin cohaerere = stick together, to be connected with). ... For other uses, see Wavelength (disambiguation). ... This article is about a portion of a periodic process. ...

The total phase difference is derived from the sum of both the path difference and the initial phase difference (if the waves are generated from 2 or more different sources). It can then be concluded whether the waves reaching a point are in phase (constructive interference) or out of phase (destructive interference).

## Contents  Chromatic interference is seen in sea foam, which is made out of plankton. It is a sample of the naturally occurring interference.

This form of interference can occur whenever a wave can propagate from a source to a destination by two or more paths of different length. Two or more sources can only be used to produce interference when there is a fixed phase relation between them, but in this case the interference generated is the same as with a single source; see Huygens' principle. Huygens principle (named for Dutch physicist Christiaan Huygens) is a method of analysis applied to problems of wave propagation. ...

## Experiments

Thomas Young's double-slit experiment showed interference phenomena where two beams of light which are coherent interfere to produce a pattern. Thomas Young, English scientist Thomas Young (June 13, 1773-May 10, 1829) was an English polymath, contributing to the scientific understanding of vision, light, solid mechanics, energy, physiology, and Egyptology. ... Slit experiment redirects here. ...

The beams of light both have the same wavelength range and at the center of the interference pattern. They have the same phases at each wavelength, as they both come from the same source. This article is about a portion of a periodic process. ...

## Constructive and destructive interference

Consider two waves that are in phase,with amplitudes A1 and A2. Their troughs and peaks line up and the resultant wave will have amplitude A = A1 + A2. This is known as constructive interference. Image File history File linksMetadata Michelson_Interferometer_Green_Laser_Interference. ... Image File history File linksMetadata Michelson_Interferometer_Green_Laser_Interference. ... A Michelson interferometer for use on an optical table. ...

If the two waves are π radians, or 180°, out of phase, then one wave's crests will coincide with another wave's troughs and so will tend to cancel out. The resultant amplitude is A = | A1A2 | . If A1 = A2, the resultant amplitude will be zero. This is known as destructive interference. For the musical group, see Radian (band). ...

When two sinusoidal waves superimpose, the resulting waveform depends on the frequency (or wavelength) amplitude and relative phase of the two waves. If the two waves have the same amplitude A and wavelength the resultant waveform will have an amplitude between 0 and 2A depending on whether the two waves are in phase or out of phase.

 combined waveform wave 1 wave 2 Two waves in phase Two waves 180° out of phase

diagram drawn by Theresa Knott File links The following pages link to this file: Interference Categories: GFDL images ...

## General quantum interference  Two point interference in a ripple tank.
Quantum mechanics $Delta x Delta p ge frac{hbar}{2}$
Uncertainty principle
Introduction to...

Mathematical formulation of... Image File history File linksMetadata Size of this preview: 397 Ã— 599 pixelsFull resolution (1024 Ã— 1544 pixel, file size: 175 KB, MIME type: image/jpeg)Photographer: Armedblowfish License: BSD Date taken: 2006, sometime during or around May Camera: Film, Nikon N65 Lens: Nikon 28-80 mm f/3. ... Image File history File linksMetadata Size of this preview: 397 Ã— 599 pixelsFull resolution (1024 Ã— 1544 pixel, file size: 175 KB, MIME type: image/jpeg)Photographer: Armedblowfish License: BSD Date taken: 2006, sometime during or around May Camera: Film, Nikon N65 Lens: Nikon 28-80 mm f/3. ... Wikibooks has more about this subject: School science how-to In physics and engineering, a ripple tank is a shallow glass tank of water used in schools and colleges to demonstrate the basic properties of waves. ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ... This box:      Werner Heisenberg and Erwin SchrÃ¶dinger, founders of Quantum Mechanics. ... The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. ...

Fundamental concepts
Quantum state · Wave function
Superposition · Entanglement

Measurement · Uncertainty
Exclusion · Duality
Decoherence · Ehrenfest theorem · Tunneling Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... Bra-ket notation is the standard notation for describing quantum states in the theory of quantum mechanics. ... The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space (or, in the case of ensembles, as a trace class operator with trace 1). ... Probability densities for the electron at different quantum numbers (l) In quantum mechanics, the quantum state of a system is a set of numbers that fully describe a quantum system. ... A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ... Quantum superposition is the application of the superposition principle to quantum mechanics. ... It has been suggested that Quantum coherence be merged into this article or section. ... The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications. ... In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ... This box:      In physics and chemistry, waveâ€“particle duality is the concept that all matter exhibits both wave-like and particle-like properties. ... In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior - a feature of classical physics - and give the appearance of wavefunction collapse. ... The Ehrenfest theorem, named after Paul Ehrenfest, relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system. ... In quantum mechanics, quantum tunnelling is a micro and nanoscopic phenomenon in which a particle violates principles of classical mechanics by penetrating or passing through a potential barrier or impedance higher than the kinetic energy of the particle. ...

This box: view  talk  edit $|psi rang = sum_i |irang psi_i$

where the $|irang$s specify the different quantum "alternatives" available (technically, they form an eigenvector basis) and the ψi are the probability amplitude coefficients, which are complex numbers. In linear algebra, the eigenvectors (from the German eigen meaning own) of a linear operator are non-zero vectors which, when operated on by the operator, result in a scalar multiple of themselves. ... In linear algebra, a basis is a set of vectors that, in a linear combination, can represent every vector in a given vector space, and such that no element of the set can be represented as a linear combination of the others. ... In quantum mechanics, a probability amplitude is a complex-valued function that describes an uncertain or unknown quantity. ... The complex numbers are an extension of the real numbers, in which all non-constant polynomials have roots. ...

The probability of observing the system making a transition or quantum leap from state Ψ to a new state Φ is the square of the modulus of the scalar or inner product of the two states: Quantum Leap is a science fiction television series that ran for 97 episodes from March 1989 to May 1993 on NBC. It follows the adventures of Dr. Samuel Beckett (played by Scott Bakula), a brilliant scientist who after researching time-travel, and doing experiments in something he calls The Imaging... In mathematics, the dot product (also known as the scalar product and the inner product) is a function (·) : V × V → F, where V is a vector space and F its underlying field. ... In mathematics, an inner product space is a vector space with additional structure, an inner product (also called a scalar product), which allows us to introduce geometrical notions such as angles and lengths of vectors. ...

where $psi_i = lang i|psi rang$ (as defined above) and similarly $phi_i = lang i|phi rang$ are the coefficients of the final state of the system. * is the complex conjugate so that $psi_i^* = lang psi|i rang$, etc. In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. ...

Now let's consider the situation classically and imagine that the system transited from $|psi rang$ to $|phi rang$ via an intermediate state $|irang$. Then we would classically expect the probability of the two-step transition to be the sum of all the possible intermediate steps. So we would have

The classical and quantum derivations for the transition probability differ by the presence, in the quantum case, of the extra terms $sum_{ij;i ne j} psi^*_i psi_j phi^*_jphi_i$; these extra quantum terms represent interference between the different $i ne j$ intermediate "alternatives". These are consequently known as the quantum interference terms, or cross terms. This is a purely quantum effect and is a consequence of the non-additivity of the probabilities of quantum alternatives.

The interference terms vanish, via the mechanism of quantum decoherence, if the intermediate state $|irang$ is measured or coupled with the environment. In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior - a feature of classical physics - and give the appearance of wavefunction collapse. ...

## Examples

A conceptually simple case of interference is a small (compared to wavelength) source - say, a small array of regularly spaced small sources (see diffraction grating). To meet Wikipedias quality standards, this article or section may require cleanup. ...

Consider the case of a flat boundary (say, between two media with different or simply a flat mirror), onto which the plane wave is incident at some angle. In this case of continuous distribution of sources, constructive interference will only be in specular direction - the direction at which angle with the normal is exactly the same as the angle of incidence. Thus, this results in the law of reflection which is simply the result of constructive interference of a plane wave on a plane surface. A specular highlight on a rendered sphere. ... The reflection of sunlight on water Reflection is the abrupt change in direction of a wave front at an interface between two dissimilar media so that the wave front returns into the medium from which it originated. ...

In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies. ... It has been suggested that Line moirÃ© be merged into this article or section. ... Interferometry is the applied science of combining two or more input points of a particular data type, such as optical measurements, to form a greater picture based on the combination of the two sources. ... // Field and linear interferometers Fabry-Perot Michelson interferometer Mach-Zehnder interferometer Sagnac interferometer Double-slit interferometer Fourier-transform interferometer Astronomical interferometer / Michelson stellar interferometer Mireau interferometer (also known as a Mireau objective) (microscopy) Multi-beam interferometer (microscopy) Watson interferometer (microscopy) Linnik interferometer (microscopy) Diffraction-grating interferometer (white light) Gires-Tournois... Coherence is the property of wave-like states that enables them to exhibit interference. ... In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior - a feature of classical physics - and give the appearance of wavefunction collapse. ... Optical feedback Credit: Profero Graphics Two Screenshots of optical feedback Credit: Profero Graphics Optical feedback is the optical equivalent of acoustic feedback. ... The intensity pattern formed on a screen by diffraction from a square aperture Diffraction refers to various phenomena associated with wave propagation, such as the bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. ... There are very few or no other articles that link to this one. ... Active noise control (ANC) (also known as noise cancellation, active noise reduction (ANR) or antinoise) is a method for reducing unwanted sound. ... Results from FactBites:

 Interference - Wikipedia, the free encyclopedia (512 words) Interference is the superposition of two or more waves resulting in a new wave pattern. As most commonly used, the term usually refers to the interference of waves which are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. However, in general white light is less suited for producing clear interference patterns, as it is a mix of a full spectrum of colours, that each have different spacing of the interference fringes.
 Interference - definition of Interference in Encyclopedia (514 words) In communications, interference is anything which alters, modifies, or disrupts a message; as it travels along a channel, between a source and a receiver. Interference is involved in Thomas Young's double-slit experiment where coherent light (light which is in the same phase, and has the same frequency and wavelength) interferes to produce an interference pattern. When a single source interferes with itself, the principle of conservation of energy dictates that the energy "missing" from the darkened regions of an interference pattern where destructive interference has taken place will be found in the brightened portions where constructive interference has taken place.
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