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

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