Semiclassical Asymptotics of Solutions of Two-Term Equation of Mathieu Type

Student: Valieva Rushana

Supervisor: Evgeny Vybornyi

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Year of Graduation: 2021

In this paper, a one-dimensional Schrödinger equation with a periodic potential of the Mathieu type is studied. We investigate the Stokes lines and the canonical domains bounded by them and construct the asymptotics of the differential equation. To find the asymptotics we use method of semiclassical approximation in the complexplane and the method of differential equations with periodic coefficients. As a result, an asymptotic formula was obtained for the width of the instability zones in the case of a two-term potential of the Mathieu type.

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