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 (qM + gqN), where N > M > 0 even, and g > 0. Mainly, we establish the g → 0 limiting forms of global spectral functions such as the zeta-regularized determinants and some spectral zeta functions.
Cite this article
André Voros, From Exact-WKB towards Singular Quantum Perturbation Theory. Publ. Res. Inst. Math. Sci. 40 (2004), no. 3, pp. 973–990DOI 10.2977/PRIMS/1145475499