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TMF, 2006, Volume 146, Number 3, Pages 410–428 (Mi tmf2044)  

Semicrystal with a singular potential in an accelerating electric field

A. A. Pozharskii

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: We study the Schrödinger equation describing the one-dimensional motion of a quantum electron in a periodic crystal placed in an accelerating electric field. We describe the asymptotic behavior of equation solutions at large values of the argument. Analyzing the obtained asymptotic expressions, we present rather loose conditions on the potential under which the spectrum of the corresponding operator is purely absolutely continuous and spans the entire real axis.

Keywords: Schrödinger equation, asymptotic solution, adiabatic solution, turning point, absolutely continuous spectrum

DOI: https://doi.org/10.4213/tmf2044

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English version:
Theoretical and Mathematical Physics, 2006, 146:3, 343–360

Bibliographic databases:

Received: 28.03.2005
Revised: 23.08.2005

Citation: A. A. Pozharskii, “Semicrystal with a singular potential in an accelerating electric field”, TMF, 146:3 (2006), 410–428; Theoret. and Math. Phys., 146:3 (2006), 343–360

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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