From exact-WKB towards singular quantum perturbation theory

Abstract

We use exact WKB analysis to derive some concrete formulae in singular quantum perturbation theory, for Schrödinger eigenvalue problems on the real line with polynomial potentials of the form $(q^M+g{q}^N)$, where $N>M>0$ even, and $g>0$. Mainly, we establish the $g\to 0$ limiting forms of global spectral functions such as the zeta-regularized determinants and some spectral zeta functions.

latex text.tex, 3 files, 2 figures, 14 pages http://www-spht.cea.fr/articles/T03/192 [SPhT-T03/192], submitted to Publ. RIMS, Kyoto Univ. (special 40th anniversary issue)

References in corpus (1)

• Functional relations in Stokes multipliers - Fun with $x^6+\alpha x^2$ potential-

Cited by in corpus (2)

• From exact-WKB toward singular quantum perturbation theory II
• Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group