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TMF, 2018, Volume 197, Number 3, Pages 464–474 (Mi tmf9573)  

Calculation of the discrete spectrum of some two-dimensional Schrödinger equations with a magnetic field

A. V. Marikhinaa, V. G. Marikhinb

a Lomonosov Moscow State University, Moscow, Russia
b Landau Institute for Theoretical Physics, Chernogolovka, Moscow Oblast, Russia

Abstract: One of us previously obtained and integrated the first examples of two-dimensional Schrödinger equations with a magnetic field belonging to the class of quasi–exactly solvable problems. It was shown that the wave functions are expressed in terms of degenerations of the Heun function: biconfluent and confluent Heun functions. Algebraic conditions were also found that determine the discrete spectrum and wave functions. Our goal here is to solve these algebraic equations numerically. In some cases, we can find an analytic approximation of the discrete spectrum.

Keywords: quantum mechanics, Heun function, quasi–exactly solvable problem.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00289
The research of V. G. Marikhin was supported by the Russian Foundation for Basic Research (Grant No. 16-01-00289).


DOI: https://doi.org/10.4213/tmf9573

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English version:
Theoretical and Mathematical Physics, 2018, 197:3, 1797–1805

Bibliographic databases:

Received: 02.04.2018

Citation: A. V. Marikhina, V. G. Marikhin, “Calculation of the discrete spectrum of some two-dimensional Schrödinger equations with a magnetic field”, TMF, 197:3 (2018), 464–474; Theoret. and Math. Phys., 197:3 (2018), 1797–1805

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