S. A. S. Ahmed, “A Transformation Method of Generating Exact Analytic Solutions of the Schrodinger Equation,” International Journal of Theoretical Physics, Vol. 36, No. 8, 1997, pp. 1893-1905. doi:10.1007/BF02435851

has been cited by the following article:

• 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.