Exactly solvable potentials and the bound-state solution of the position-dependent mass Schrödinger equation in $D$-dimensional space

We propose a transformation method using properties of classical orthogonal polynomials to construct exactly solvable potentials that provide bound-state solutions of Schrödinger equations with a position-dependent mass in $D$-dimensional space. The important feature of the method is that it favors the Zhu–Kroemer ordering of ambiguities for a radially symmetric mass function and potential. This is illustrated using hypergeometric polynomials and the associated Legendre polynomials.