Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial
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A. Fedotov and E. Shchetka
Translated by: A. Fedotov - St. Petersburg Math. J. 29 (2018), 363-381
- DOI: https://doi.org/10.1090/spmj/1497
- Published electronically: March 12, 2018
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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 $h\to 0$.References
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Bibliographic Information
- A. Fedotov
- Affiliation: St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg 199034, Russia
- Email: a.fedotov@spbu.ru
- E. Shchetka
- Affiliation: St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg 199034, Russia
- Email: shchetka.ekaterina@mail.ru
- 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.
- © Copyright 2018 American Mathematical Society
- Journal: St. Petersburg Math. J. 29 (2018), 363-381
- MSC (2010): Primary 34E20
- DOI: https://doi.org/10.1090/spmj/1497
- MathSciNet review: 3660678
Dedicated: Dedicated to the memory of Vladimir Savel’evich Buslaev