The derivation of 1/N equivalent potentials for the radial Schrödinger equation in N space dimensions

Abstract

Proofs are given that SOq(N)-motivated q deformations of the expansion parameter of the 1/N method can be incorporated into symmetry transformations preserving the radial form of the Schrödinger equation. This opens the way to establish the q deformed energy and the corresponding 1/N equivalent potential. So far the number of space dimensions is subject of covariant transformations. An alternative derivation of the 1/N equivalent potential is also done by keeping this number invariant. In this latter case, the stability attributes of q-deformed power-law potentials are discussed in terms of the q > 1 choice.