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.


References in periodicals archive ?
In the heavy nuclei for which the anapole moment is a well-defined observable, the main contribution to the anapole moment comes from PV admixtures in the nuclear ground state wave function.
In fact, a macroscopic system described by quantum mechanics with the linear Schrodinger equation dictating the time evolution of the wave function is more predictable than a classical chaotic system.
YAMASHITA, On eigenvalues of spheroidal wave function, Proceedings of the 23rd Numerical Analysis Symposium, (1993), pp.
It's sort of an axiom of quantum mechanics that the wave function can tell you absolutely all you want to know about a [quantum] system," he adds.
A1] between the partial wave functions can be superimposed.
Information is, in some way, encoded in the wave function, or some sort of a field of form, or some set of prequantum algebraic relationships.
spatial localisation of the electron wave functions tunneling through a 10 nm quantum barrier, when the diode is operated in reverse bias.
As a slit size decreases, the neutron wave function [[psi].
Using supercomputers at the Berkeley and Lawrence Livermore National Laboratories, McCurdy and his colleagues calculated the wave function for the simplest such collision.
A convenient wavelength for discussion on wave function is that of red and infrared parts of the spectrum, some three orders of magnitude greater, familiar as the heat range at about one micron in length.