Exact solution of D-dimensional Schrödinger equation generated from certain central power-law potentials

Abstract

AbstractBy applying Extended Transformation method we have generated exact solution of D-dimensional radial Schrödinger equation for a set of power-law multi-term potentials taking singular potentials $$V(r) = ar^{ - \tfrac{1} {2}} + br^{ - \tfrac{3} {2}}$$, $$V(r) = ar^{\tfrac{2} {3}} + br^{ - \tfrac{2} {3}} + cr^{ - \tfrac{4} {3}}$$, V(r) = ar + br−1 + cr2 and V(r) = ar2+br−2+cr−4+dr−6 as input reference. The restriction on the parameters of the given potentials and angular momentum quantum number ℓ are obtained. The multiplet structure of the generated exactly solvable potentials are also shown.