The Open Applied Mathematics Journal

2009, 3 : 29-32
Published online 2009 September 04. DOI: 10.2174/1874114200903010029
Publisher ID: TOAMJ-3-29

The Darboux Transform Applied to Schrödinger Equations with a Position-Dependent Mass

G. Ovando , J. Morales , J.J. Peña , G. Ares de Parga and J.L. López-Bonilla
Universidad Autónoma Metropolitana - Azcapotzalco, CBI - Area de Física Atómica Molecular Aplicada, Av. San Pablo 180, Reynosa Azcapotzalco, 02200 México, D. F.

ABSTRACT

Essentially, the Darboux proposition is based on the covariance properties of ordinary and partial differential equations with respect to a gauge transformation in the special case of second order differential equations of the Sturm- Liouville type. In this work, the one-dimensional Schrödinger equation with a position-dependent mass (SEPDM) is transformed into a Schrödinger-like equation with a position-independent mass (SLEPIM) for an effective potential which incorporates the spatially dependent mass. Therefore, taking advantage of the similarity between the SLEPIM and the Sturm-Liouville differential equation it is shown the application of the Darboux transform to the SEPDM problem.

Keywords:

Darboux transform, Schrödinger equation, position-dependent mass.