Separation of Coupled Systems of Schrodinger Equations by Darboux transformations

TL;DR

This paper extends Darboux transformations to two dimensions to decouple coupled Schrödinger systems, providing explicit solutions and revealing connections to complex matrix functions, advancing mathematical physics methods.

Contribution

It introduces a novel extension of Darboux transformations to two-dimensional systems and explicitly decouples certain Schrödinger equations, linking them to complex matrix functions.

Findings

Decoupling of coupled Schrödinger systems achieved

Explicit representations for three classes of systems provided

Connection established between Darboux transformations and complex matrix functions

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.