From exact-WKB towards singular quantum perturbation theory

Details From exact-WKB towards singular quantum perturbation theory From exact-WKB towards singular quantum perturbation theory

2003-12-10

arxiv.org/abs/math-ph/0312024v1

Publ. RIMS, Kyoto Univ. 40 (2004) 973-990.

Physics

Mathematical Physics

latex text.tex, 3 files, 2 figures, 14 pages http://www-spht.cea.fr/articles/T03/192 [SPhT-T03/192], submitted to Publ. RIMS

Scientific paper

We use exact WKB analysis to derive some concrete formulae in singular quantum perturbation theory, for Schr\"odinger 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.

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