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TMF, 2004, Volume 140, Number 2, Pages 297–302 (Mi tmf94)  

Schrödinger Operator Levels for a Crystal Film with a Nonlocal Potential

M. S. Smetanina, Yu. P. Chuburin

Udmurt State University

Abstract: For a crystal film, we consider the Schrödinger operator defined on Bloch functions (with respect to two variables) in a cell. The potential is the sum of two small terms: a function decreasing with respect to the third variable and an operator of rank one. We prove the existence of two levels (eigenvalues or resonances) near the parameter value $E=0$ and obtain their asymptotic.

Keywords: Schrödinger operator, periodic potential, nonlocal potential, eigenvalue, resonance, asymptotic behavior

DOI: https://doi.org/10.4213/tmf94

Full text: PDF file (181 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 140:2, 1146–1150

Bibliographic databases:

Received: 22.09.2003
Revised: 05.01.2004

Citation: M. S. Smetanina, Yu. P. Chuburin, “Schrödinger Operator Levels for a Crystal Film with a Nonlocal Potential”, TMF, 140:2 (2004), 297–302; Theoret. and Math. Phys., 140:2 (2004), 1146–1150

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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