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TMF, 2011, Volume 168, Number 2, Pages 219–226 (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

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

DOI: https://doi.org/10.4213/tmf6676

Full text: PDF file (313 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 168:2, 1041–1047

Bibliographic databases:

Received: 13.03.2011

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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\paper Solutions of two-dimensional Schr\"odinger-type equations in a~magnetic field
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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