Separation of Coupled Systems of Schrodinger Equations by Darboux transformations

Abstract

Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple systems of Schrodinger equations and provide explicit representation for three classes of such systems. We show also that there is an elegant relationship between these transformations and analytic complex matrix functions.

14 pages

References in corpus (5)

• Algebraic Approach to Shape Invariance
• Chains of Darboux transformations for the matrix Schroedinger equation
• Klein tunneling in carbon nanostructures: a free particle dynamics in disguise
• On form-preserving transformations for the time-dependent Schrödinger equation
• The Multidimensional Darboux Transformation