# 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 ?
Table 1 displays the radial part R(Z, r) for the orbitals 1s to 6h of hydrogen-like atoms together with the corresponding radial expectation values (for Z = 1, wavefunctions taken from reference [7]).
where [I.sup.(4)] is the 4x4 unit matrix and [PSI] is a 4-component column (bispinor) wavefunction. Dirac then decomposes equation (17) by assuming them as a quadratic equation
In order to calculate the transmission (T) and reflection (R) probability densities, we use asymptotic expressions of the wavefunctions.
In the usual formulation of quantum mechanics a conserved positive-definite probability density is required for a consistent interpretation of the physical properties of a given system, and the universe in the quantum cosmology perspective, do not satisfied this requirement, because the WDW equation is a hyperbolic second order differential equation, there is no conserved positive-definite probability density as in the case of the Klein-Gordon equation, an alternative to this, is to regard the wavefunction as a quantum field in minisuperspace rather than a state amplitude [7].
Then, it is natural to introduce a wavefunction [psi] through S = -i[eta] ln [psi], where [eta] turns out to be Planck's constant.
Now as both wavefunctions [[psi].sub.1] and [[psi].sub.2] are orthogonal and distinguishable because of spatial separation (no overlap) in the interferometer arms 1 and 2, and because they get entangled with orthogonal states of the two different polarizators V and H, in the future spatial overlapping of the wavefunctions [[psi].sub.1] and [[psi].sub.2] cannot convert them into non-orthogonal states.
The quantum mechanical description of the system derived from the foregoing considerations sees the dynamical variables (q, p) now interpreted as operators [mathematical expression not reproducible] acting on complex wavefunctions [psi](q) generating observables and satisfying the commutation relation
The problem of quantum gravity is therefore to interpret GR in terms of the wavefunctions of QM.
Mostly, the environment is assumed to be the continuum of scattering wavefunctions (1).
This explains the high-spin nature of the wavefunctions for triangles.
Figures of the same as show the changes of wavefunctions in different QHO iterations.

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