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

摘要

With the consideration of spherical symmetry for the potential and massfunction, one-dimensional solutions of non-relativistic Schrodinger equationswith spatially varying effective mass are successfully extended to arbitrarydimensions within the frame of recently developed elegant non-perturbativetechnique, where the BenDaniel-Duke effective Hamiltonian in one-dimension isassumed like the unperturbed piece, leading to well-known solutions, whereasthe modification term due to possible use of other effective Hamiltonians inone-dimension and, together with, the corrections coming from the treatments inhigher dimensions are considered as an additional term like the perturbation.Application of the model and its generalization for the completeness arediscussed.