Wentzel-Kramers-Brillouin method

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Wentzel-Kramers-Brillouin method

A special technique for obtaining an approximation to the solutions of the one-dimensional time-independent Schrödinger equation, valid when the wavelength of the solution varies slowly with position. It is named after G. Wentzel, H. A. Kramers, and L. Brillouin, who independently in 1926 contributed to its understanding in the quantum-mechanical application. It is also called the WKB method, BWK method, the classical approximation, the quasi-classical approximation, and the phase integral method. See Quantum mechanics, Schrödinger's wave equation

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.

Wentzel-Kramers-Brillouin method

[′vent·səl ′krä·mərz brē′wan ‚meth·əd]
(quantum mechanics)
Method of approximating quantum-mechanical wave functions and energy levels, in which the logarithm of the wave function is expanded in powers of Planck's constant, and all except the first two terms are neglected. Also known as phase integral method; WKB method.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
(b) Higher-order WKB corrections: Using WKB approximation method, the lowest order of the equation of motion describing a particle moving in the black hole gives the Hamilton-Jacobi equation.
Using the WKB approximation the tunneling probability for the classically forbidden trajectory through the horizon is given by
Another scenario where f(R) theory has been considered is the origin of the universe by a tunneling mechanism from "nothing" to the de Sitter phase of Starobinski's model [8], where a description of the universe in the framework of quantum cosmology is given, from which the tunneling probability, the subsequent curvature fluctuations, and the duration of the inflationary phase were computed, in the WKB approximation. Quantum cosmology of f(R) theories has been studied also in [9-12].
Various methods are employed to solve singular perturbation problems analytically, numerically, or asymptotically such as the method of matched asymptotic expansions (MMAE), the method of multiple scales, the method of WKB approximation, Poincare-Lindstedt method and periodic averaging method.
extended an approximation technique of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case.
Using the WKB approximation in inhomogeneous plasma the starting point is a solution of the form
If amplitudes or phases of the solutions can be assumed as slowly varying quantities, asymptotic approaches such as the WKB approximation can be applied to find approximate wave solutions [12-16].
The semiclassical tunneling method by using the Hamilton-Jacobi ansatz with WKB approximation is another way to obtain the Bekenstein-Hawking temperature and the tunneling rate as [GAMMA] [approximately equal to] exp[-2fmS] [19].
Using the WKB approximation, the action can be chosen at the leading order in [??] as
Then, they used the WKB approximation to show that the solution to the deformed Schrodinger equation:
(iii) We employ the WKB approximation [45, 46] to evaluate the quasinormal frequencies.
Most famous derivation is made by Parikh and Wilczek in which they use a tunnelling process with a semiclassical WKB approximation [4-12].