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

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

2002-01-24

arxiv.org/abs/math-ph/0201052v1

Proceedings ed. by BLJ Braaksma et al., World Scientific (2002) pp.293-308.

Physics

Mathematical Physics

latex txt12.tex, 4 files, 3 figures, 18 pages Differential equations and Stokes phenomenon Groningen, The Netherlands May 28-3

Scientific paper

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.

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