Wave Function

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wave function

[′wāv ‚fəŋk·shən]
(quantum mechanics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Wave Function

 

in quantum mechanics, a quantity that completely describes the state of a microscopic object (for example, an electron, proton, atom, or molecule) and of any quantum system (for example, a crystal) in general.

A description of the state of a microscopic object by means of the wave function is statistical, or probabilistic, in character: the square of the absolute value (modulus) of a wave function indicates the probability of those quantities on which the wave function depends. For example, if the dependence of the wave function of a particle on the coordinates x, y, and z and on time t is given, then the square of the absolute value of this wave function defines the probability of finding the particle at time t at a point with coordinates jc, y, z. Insofar as the probability of the state is defined by the square of the wave function, the latter is also called the amplitude of probability.

At the same time, a wave function also reflects the presence of wave characteristics in microscopic objects. Thus, for a free particle with given momentum p and energy δ. to which a de Broglie wave with a frequency v = δ/h and a wavelength λ = h/p (where h is Planck’s constant) is compared, the wave function must be periodic in space and time, with the corresponding value of X and a period T = l/v.

The superposition principle is valid for wave functions. If a system may be found in various states with wave functions ψ1, ψ22, .… , then a state with a wave function equal to the sum—and in general, to any linear combination—of these wave functions is also possible. The addition of wave functions (amplitudes of probability), but not of probabilities (the squares of wave functions), fundamentally distinguishes quantum theory from any classical statistical theory in which the theorem of the addition of probabilities is valid.

The properties of the symmetry of wave functions, which define the statistics of the aggregate of particles, are essential to systems consisting of many identical microparticles.

V. I. GRIGOR’EV

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
The transverse distortion wave [[omega].sup.[mu]v] corresponds to a multi-component wavefunction [PSI].
Rabitz, "Quantum wavefunction controllability," Chemical Physics, vol.
where [psi](r) is the wavefunction, |k> is the incident wave, G is the one-body Green's function, and v is the optical potential.
The software package we will use for the Computational Organic Lab was obtained from WaveFunction Inc.
At the start of his seminal 1957 discussion, Everett makes it clear that no a priori interpretation of the wavefunction is assumed in his scheme.
He shows that quantum field theory arises naturally from quantum mechanics by recognizing that the fock-space representation is the obvious way of implementing the (anti) symmetry of the wavefunction, and then allowing states with indefinite numbers of quanta.
In [87], the decay constant and distribution amplitude for the heavy-light pseudoscalar mesons have been evaluated using the light-front holographic wavefunction. By using the Gaussian wave function with quark-antiquark potential model, the Regge trajectories, spectroscopy, and decay properties have been studied for B and [B.sub.s] mesons [88], D and [D.sub.s] mesons [89], and also the radiative transitions and the mixing parameters of the D-meson have been obtained [90].
These mappings occur only together in a spatiotemporally symmetric metaprocess called conspansion, where they define primary (potentiative) and secondary (actualizative) stages of causation respectively associated with wavefunction propagation and collapse.
Sherrill, "Wavefunction methods for noncovalent interactions," Wiley Interdisciplinary Reviews: Computational Molecular Science, vol.
The wavefunction [[psi].sub.i]([r.sub.1]) represents the incident electron, [[phi].sub.i]([r.sub.2]) the inner shell electron, [[psi].sub.f]([r.sub.1]) the scattered electron and [[phi].sub.f]([r.sub.2]) the ejected electorn.
(7) Once the robustness of the synthesized molecule is guaranteed, it could be described by its quantum wavefunction supplemented by boundary conditions.