Explicit Solutions for N-Dimensional Schrodinger Equations with Position-Dependent Mass

Abstract

With the consideration of spherical symmetry for the potential and mass function, one-dimensional solutions of non-relativistic Schrodinger equations with spatially varying effective mass are successfully extended to arbitrary dimensions within the frame of recently developed elegant non-perturbative technique, where the BenDaniel-Duke effective Hamiltonian in one-dimension is assumed like the unperturbed piece, leading to well-known solutions, whereas the modification term due to possible use of other effective Hamiltonians in one-dimension and, together with, the corrections coming from the treatments in higher dimensions are considered as an additional term like the perturbation. Application of the model and its generalization for the completeness are discussed.