English

"Exact WKB integration'' of polynomial 1D Schr\"odinger (or Sturm-Liouville) problem

Mathematical Physics 2007-05-23 v1 math.MP

Abstract

We review an "exact semiclassical" resolution method for the general stationary 1D Schr\"odinger equation with a polynomial potential. This method avoids having to compute any Stokes phenomena directly; instead, it basically relies on an elementary Wronskian identity, and on a fully exact form of Bohr--Sommerfeld quantization conditions which can also be viewed as a Bethe-Ansatz system of equations that will "solve" the general polynomial 1D Schr\"odinger problem.

Keywords

Cite

@article{arxiv.math-ph/0201052,
  title  = {"Exact WKB integration'' of polynomial 1D Schr\"odinger (or Sturm-Liouville) problem},
  author = {A. Voros},
  journal= {arXiv preprint arXiv:math-ph/0201052},
  year   = {2007}
}

Comments

latex txt12.tex, 4 files, 3 figures, 18 pages Differential equations and Stokes phenomenon Groningen, The Netherlands May 28-30 2001 [SPhT-T01/146]