# Wave Function

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## wave function

[′wāv ‚fəŋk·shən]
(quantum mechanics)

## 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

References in periodicals archive ?
From these observation data, we computed the corresponding heat wave function by inverting the heat transform using the semi-smooth Newton method from Section 4.
The Canadian scientists claim that their new method of probing molecular structure has yielded the most revealing image so far of an electron's wave function. This function depicts both the amplitude and direction of an electron wave's oscillations at every point in space.
that the partial wave function of a neutron of kinetic energy [E.sub.k] = [h.sup.2][k.sup.2]/2m experiences when passing through a sample of thickness d.
Harmonic spectra obtained at 19 different angles were analyzed and the 3D shape of the molecule's wave function was derived.
Rather, the intrinsic properties, described by the wave function, determine the way in which the probabilistic laws act on a system.(2) One should think of the relationship between a system's quantum state and its probabilistic dynamics in exactly the way that one thinks of the relation between a particle's mass and its deterministic dynamics in Newtonian mechanics.
It causes the discontinuity conditions for the derivative of the wave functions. The probability current for each region of our considered problem was determined.
The WDW equation has been analyzed with different approaches in order to solve it, and there are several papers on the subject, such is the case in [28], where they debate what a typical wave function for the universe is.
To resolve this seeming paradox, and make all these predictions of quantum theory applied to the two observers O and O' respectively consistent requires that any wave function of a system S be defined relative to the observer.
One of the main problems concerning quantum physics is how to interpret Schrodinger's wave function and the way it describes the physical world.
As the physicists explain, in order for two independently prepared, identical particles to be entangled, they must share a region of space in close physical proximity--more technically, the particles' wave functions must spatially overlap, at least partially.
Wave functions are functions of both time and space and can change as time progresses.
Two-center Franck-Condon (FC) integral over harmonic oscillators wave functions have the following form:

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