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.