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arXiv · 1903.05201

WKB and "Cubic-WKB" methods as an adiabatic approximation

Shinji Iida
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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".

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Shinji Iida. 2019-03-11. WKB and "Cubic-WKB" methods as an adiabatic approximation. https://doi.org/10.1142/s021773231950250x

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