We apply the extended transformation method, comprising a coordinate transformation supplemented by a functional transformation, to generate (regenerate) exactly solvable ring-shaped potentials from already known exactly solvable central potentials for physical quantum systems in a non-relativistic regime. The angular wave functions corresponding to the generated potentials are transformed from the radial wave functions of the original central potentials in a very straightforward way and they are also shown to be normalizable.

No abstract

We propose a method for construction of exactly solvable ring-shaped potentials where the linear homogeneous second-order differential equation satisfied by special function is subjected to the extended transformation comprising a coordinate transformation and a functional transformation to retrieve the standard Schr?dinger polar angle equation form in non-relativistic quantum mechanics. By invoking plausible ansatze, exactly solvable ring-shaped potentials and corresponding angular wave functions are constructed. The method is illustrated using Jacobi and hypergeometric polynomials and the wave functions for the constructed ring-shaped potentials are normalized.

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.