TITLE:
Construction of Exactly Solvable Ring-Shaped Potentials
AUTHORS:
Arup Bharali, Ngangkham Nimai Singh
KEYWORDS:
Schrödinger Equation; Extended Transformation; Special Function; Ring-Shaped Potential; Normalization
JOURNAL NAME:
Journal of Modern Physics,
Vol.4 No.4,
April
19,
2013
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.