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Divergence-free WKB method

Tadanori Hyouguchi·Satoshi Adachi·Masahito Ueda
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Abstract

A new semiclassical approach to linear (L) and nonlinear (NL) one-dimensional Schrödinger equation (SE) is presented. Unlike the usual WKB solution, our solution does not diverge at the classical turning point. For LSE, our zeroth-order solution, when expanded in powers of \hbar, agrees with the usual WKB solution. For NLSE, our zeroth-order solution includes quantum corrections to the Thomas-Fermi solution, thereby giving a smoothly decaying wave function into the forbidden region.

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Tadanori Hyouguchi, Satoshi Adachi, Masahito Ueda. 2000-11-22. Divergence-free WKB method. https://arxiv.org/abs/cond-mat/0011374

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