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Article

WKB Asymptotics and Spectral Deformation in Semi-classical Limit

Journal of Dynamical and Control Systems. 2020. Vol. 26. No. 1. P. 175-198.
Fufaev V., Степин С. А.

Phase-integral method is applied to study semi-classical limit for the spectral problem related to dynamical system describing quantum mechanical evolution with space-time reflection symmetry. The main goal of the paper is to investigate the relationship between analytic properties of the corresponding potential and the structure of limiting spectral graph. Quantization conditions of Bohr-Sommerfeld type are derived specifying localization of the spectrum for the model problem with a one-parameter family of polynomial potentials treated as deformation of a linear one.