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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 168, Number 2, Pages 219–226
DOI: https://doi.org/10.4213/tmf6676 (Mi tmf6676) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Solutions of two-dimensional Schrödinger-type equations in a magnetic field

V. G. Marikhin

Landau Institute for Theoretical Physics, RAS, Moscow, Russia
Full-text PDF (313 kB) Citations (1)
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DOI: https://doi.org/10.4213/tmf6676
Abstract: We use the method of dressing by a linear operator of general form to construct new solutions of Schrödinger-type two-dimensional equations in a magnetic field. In the case of a nonunit metric, we integrate the class of solutions that admit a variable separation before dressing. In particular, we show that the ratio of the coefficients of the differential operators in the unit metric case satisfies the Hopf equation. We establish a relation between the solutions of the two-dimensional eikonal equation with the unit right-hand side and solutions of the Hopf equation.
Keywords: dressing method, quantum operators, Hopf equation, eikonal equation.
Received: 13.03.2011
English version:
Theoretical and Mathematical Physics, 2011, Volume 168, Issue 2, Pages 1041–1047
DOI: https://doi.org/10.1007/s11232-011-0086-y
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. G. Marikhin, “Solutions of two-dimensional Schrödinger-type equations in a magnetic field”, TMF, 168:2 (2011), 219–226; Theoret. and Math. Phys., 168:2 (2011), 1041–1047
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6676
  • https://doi.org/10.4213/tmf6676
  • https://www.mathnet.ru/eng/tmf/v168/i2/p219
    • This publication is cited in the following 1 articles:
    1. R. A. Gabiev, A. B. Shabat, “Differential operators commuting in the principal part”, Theoret. and Math. Phys., 171:1 (2012), 435–441  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    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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    Abstract page:548
    Full-text PDF :220
    References:82
    First page:23
     
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