English

Divergence-free WKB method

Condensed Matter 2007-05-23 v1

Abstract

A new semiclassical approach to linear (L) and nonlinear (NL) one-dimensional Schr\"odinger 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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Cite

@article{arxiv.cond-mat/0011374,
  title  = {Divergence-free WKB method},
  author = {Tadanori Hyouguchi and Satoshi Adachi and Masahito Ueda},
  journal= {arXiv preprint arXiv:cond-mat/0011374},
  year   = {2007}
}

Comments

7pages 5figures revtex