"Exact WKB integration'' of polynomial 1D Schrödinger (or Sturm-Liouville) problem
A. Voros
Abstract
We review an "exact semiclassical" resolution method for the general stationary 1D Schrödinger 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 Schrödinger problem.
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