New Method for Mapping of Exact Analytic S-wave Solutions for Regenerated Central Hyperbolic Potentials

Abstract

We present a new method in the framework of non-relativistic quantum mechanics for mapping of exact analytic s-wave solutions for hyperbolic central potentials from the angular wave functions of already known quantum systems with exactly solvable ring-shaped potentials. The method is based on a coordinate redesignation and a coordinate transformation supplemented by a functional transformation. Invocation of plausible ansatz is indispensable to (re)generate hyperbolic central potentials, and the radial wave functions for the generated central potentials are shown to be normalizable elegantly.