Isospectral potentials for the Schrödinger equation with a position‐dependent mass: Free‐particle potential model

Abstract

ABSTRACT:In this work, a method to obtain exactly solvable potentials for the one-dimensional Schrödinger equation with a position-dependent mass (SEPDM) and a procedure to determine their isospectral potential partners are presented. In the first case, the problem of exactly solvable SEPDM is worked by means of the point canonical transformation method which permit to convert the SEPDM problem into a standard Schrödinger-like equation with a position-independent mass (SLEPIM). In the second case, the procedure to obtain the partner isospectral potentials that fulfill with the SEPDM involves the Darboux transform applied to the SLEPIM. As example of the usefulness of the proposals, it is considered the special case of the free particle potential model as former potential of the SEPDM which leads to different exactly solvable potentials, and to their isospectral partners, depending on the choice of the position-dependent mass distribution. The proposals are general and can be used in the search of those potentials leading to exactly solvable SEPDM and their isospectral partners, which could be useful in the modeling of quantum chemical properties in condensed matter applications.