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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial

Authors: A. Fedotov and E. Shchetka
Translated by: A. Fedotov
Original publication: Algebra i Analiz, tom 29 (2017), nomer 2.
Journal: St. Petersburg Math. J. 29 (2018), 363-381
MSC (2010): Primary 34E20
Published electronically: March 12, 2018
MathSciNet review: 3660678
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Abstract | References | Similar Articles | Additional Information

Abstract: The difference Schrödinger equation $\psi (z+h)+\psi (z-h)+ v(z)\psi (z)=E\psi (z)$, $z\in \mathbb {C}$, is considered; here $h$ is a positive number, $E$ is the spectral parameter, and $v$ is a trigonometric polynomial. The asymptotics of its entire solutions is studied as $h\to 0$.

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Additional Information

A. Fedotov
Affiliation: St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg 199034, Russia

E. Shchetka
Affiliation: St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg 199034, Russia

Keywords: Difference Schrödinger equation, complex WKB method
Received by editor(s): October 10, 2016
Published electronically: March 12, 2018
Additional Notes: Supported by RFBR (grant no. 17-01-00668-a) and by the “Möbius Contest”, a foundation for support of young scientists.
Dedicated: Dedicated to the memory of Vladimir Savel’evich Buslaev
Article copyright: © Copyright 2018 American Mathematical Society