WKB and "Cubic-WKB" methods as an adiabatic approximation
Quantum Physics
2021-06-08 v2 High Energy Physics - Theory
Abstract
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".
Cite
@article{arxiv.1903.05201,
title = {WKB and "Cubic-WKB" methods as an adiabatic approximation},
author = {Shinji Iida},
journal= {arXiv preprint arXiv:1903.05201},
year = {2021}
}