aqora

WKB and “cubic-WKB” methods as an adiabatic approximation

Shinji Iida

This paper shows that WKB wave function can be expressed in the form of an adiabatic expansion. To build a bridge between two widely invoked approximation schemes seems pedagogically instructive. Further, “cubic-WKB” method that has been devised in order to overcome the divergence problem of WKB can be also presented in the form of an adiabatic approximation: The adiabatic expansion of a wave function contains a certain parameter. When this parameter is adjusted so as to make the next order correction vanish approximately, the adiabatic wave function becomes equivalent to that of the “cubic-WKB”.This paper shows that WKB wave function can be expressed in the form of an adiabatic expansion. To build a bridge between two widely invoked approximation schemes seems pedagogically instructive. Further, “cubic-WKB” method that has been devised in order to overcome the divergence problem of WKB can be also presented in the form of an adiabatic approximation: The adiabatic expansion of a wave function contains a certain parameter. When this parameter is adjusted so as to make the next order correction vanish approximately, the adiabatic wave function becomes equivalent to that of the “cubic-WKB”.

arXiv:1903.05201Modern Physics Letters AJun 18, 20190 citations

WKB wave functions without matching

M. Casas, Angel Ricardo Plastino, Antonio Puente +2 more

A method is presented for the construction of WKB wave functions that avoids explicit consideration of any matching between results pertaining to classically allowed and classically forbidden regions. The formalism is based on the maximization of a suitably defined quantal pseudoentropy, subject to the constraints posed by the expectation values of a reduced number of operators, which are evaluated according to special WKB techniques that consider expansions up to orders \ensuremath{\Elzxh} and ${\mathrm{\ensuremath{\Elzxh}}}^{2}$. The algorithm is tested with reference to the harmonic and quartic anharmonic oscillators.A method is presented for the construction of WKB wave functions that avoids explicit consideration of any matching between results pertaining to classically allowed and classically forbidden regions. The formalism is based on the maximization of a suitably defined quantal pseudoentropy, subject to the constraints posed by the expectation values of a reduced number of operators, which are evaluated according to special WKB techniques that consider expansions up to orders \ensuremath{\Elzxh} and ${\mathrm{\ensuremath{\Elzxh}}}^{2}$. The algorithm is tested with reference to the harmonic and quartic anharmonic oscillators.

Physical Review AMay 1, 199313 citations

Normalization of WKB-Type Approximations

Stanley C. Miller

A method is developed for normalizing WKB-type approximations to wave functions for a simple potential well type of problem. The procedure closely resembles Furry's method of finding the normalization for the usual WKB approximations.

Physical ReviewJun 1, 195416 citations

Divergence-free WKB theory

Tadanori Hyouguchi, Ryohei Seto, Masahito Ueda +1 more

Annals of PhysicsMar 6, 200413 citations

Wave packets and WKB theory in phase space

Robert G. Littlejohn

A practical difficulty of traditional Wentzel-Kramer-Brillouin (WKB) theory is that it suffers from non-physical infinities at caustics. A theoretical difficulty is that it does not possess any reasonable covariance or invariance properties under transformations in phase space. It turns out that the solution of one of these problems also solves the other, and leads to a version of WKB theory in phase space. The new theory is most easily implemented by using wave packets.

Sep 1, 19860 citations

The WKB Wave Functions for the Harmonic Oscillator

H. P. Grunwald, F. Milano

American Journal of PhysicsNov 1, 19715 citations

Symplectically Invariant WKB Wave Functions

Abstract

Related papers

Symplectically Invariant WKB Wave Functions

Abstract

Related papers