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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 197, Number 3, Pages 464–474
DOI: https://doi.org/10.4213/tmf9573 (Mi tmf9573) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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
Full-text PDF (453 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf9573
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).
Received: 02.04.2018
English version:
Theoretical and Mathematical Physics, 2018, Volume 197, Issue 3, Pages 1797–1805
DOI: https://doi.org/10.1134/S0040577918120097
Bibliographic databases:
Document Type: Article
Language: Russian
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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  • https://www.mathnet.ru/eng/tmf/v197/i3/p464
    • This publication is cited in the following 3 articles:
    1. P. B. Acosta-Humánez, M. E. H. Ismail, N. Saad, “Sextic anharmonic oscillators and Heun differential equations”, Eur. Phys. J. Plus, 137:7 (2022)  crossref
    2. H. R. Rastegar Sedehi, A. Arda, R. Sever, “Thermodynamic properties of a charged particle in non-uniform magnetic field”, Opt. Quantum Electron., 53:3 (2021), 142  crossref  mathscinet  isi  scopus
    3. Geeta Arora, Varun Joshi, R. C. Mittal, “Numerical Simulation of Nonlinear Schrödinger Equation in One and Two Dimensions”, Math Models Comput Simul, 11:4 (2019), 634  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:63
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