Generation of exactly solvable potentials of the D-dimensional position-dependent mass Schrödinger equation using the transformation method

Abstract

We apply the extended transformation method to the constant-mass radial Schrodinger equation satisfied by a radially symmetric central potential in order to obtain exactly solvable quantum systems with a position-dependent mass in a space of arbitrary dimension in the nonrelativistic limit. The method consists of a coordinate transformation, a subsequent functional transformation, and a set of ansatzes for the mass function leading to the appearance of exactly solvable quantum systems with position-dependent masses. We also show that the Zhu-Kroemer ordering for the fitting parameter values is natural for systems with a radially symmetric mass function and a central potential. As an example, we apply the method to the Manning-Rosen potential and to the Morse potential with different choices of the mass functions. We also indicate an application of the method to the Hulthen potential.