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M. Zhang, G. Sun and S. Dong, “Exactly Complete Solutions of the Schrodinger Equation with a Spherically Harmonic Oscillatory Ring-Shaped Potential,” Physics Letters A, Vol. 374, No. 5, 2010, pp. 704-708. doi:10.1016/j.physleta.2009.11.072

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.