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TMF, 2016, Volume 187, Number 1, Pages 12–20 (Mi tmf8942)  

Nonlocal Darboux transformation of the two-dimensional stationary Schrödinger equation and its relation to the Moutard transformation

A. G. Kudryavtsev

Institute of Applied Mechanics, RAS, Moscow, Russia

Abstract: We consider a nonlocal Darboux transformation of the two-dimensional stationary Schrödinger equation and establish its relation to the Moutard transformation. We show that the Moutard transformation is a special case of the nonlocal Darboux transformation and obtain new examples of solvable two-dimensional stationary Schrödinger operators with smooth potentials as an application of the nonlocal Darboux transformation.

Keywords: Darboux transformation, nonlocal variable, Schrödinger equation

DOI: https://doi.org/10.4213/tmf8942

Full text: PDF file (350 kB)
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English version:
Theoretical and Mathematical Physics, 2016, 187:1, 455–462

Bibliographic databases:

PACS: 02.30.Jr, 02.30.Ik, 03.65.Ge
Received: 30.03.2015

Citation: A. G. Kudryavtsev, “Nonlocal Darboux transformation of the two-dimensional stationary Schrödinger equation and its relation to the Moutard transformation”, TMF, 187:1 (2016), 12–20; Theoret. and Math. Phys., 187:1 (2016), 455–462

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