2016•Theoretical and Mathematical PhysicsRequires access

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

A. G. Kudryavtsev

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.

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Key concepts: Transformation (genetics), Darboux integral, Mathematics, Mathematical physics, Relation (database), Schrödinger equation, Schrödinger's cat, Mathematical analysis