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

We apply the extended transformation method to the constant-mass radial Schrödinger 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.