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

André Voros (1)

1 SPhT - Service de Physique Théorique

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.

Domaines: Physique mathématique [math-ph]; Analyse classique [math.CA]

André Voros. "Exact WKB integration'' of polynomial 1D Schrödinger (or Sturm-Liouville) problem. Differential equations and the Stokes phenomenon, May 2001, Groningen, Netherlands. pp.293-308. ⟨hal-00022102⟩