This article is cited in 5 papers

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.

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

Received: 30.03.2015

DOI: 10.4213/tmf8942

 English version: Theoretical and Mathematical Physics, 2016, 187:1, 455–462

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