2013•arXiv (Cornell University)Open access

The nonlocal Darboux transformation of the 2D stationary Schrödinger equation and its relation to the Moutard transformation

A. G. Kudryavtsev

Abstract

The nonlocal Darboux transformation of the two - dimensional stationary Schrödinger equation is considered and its relation to the Moutard transformation is established. It is shown that a special case of the nonlocal Darboux transformation provides the Moutard transformation. New examples of solvable two - dimensional stationary Schrödinger operators with smooth potentials are obtained as an application of the nonlocal Darboux transformation.

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