Construction of Exactly Solvable Ring-Shaped Potentials


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.

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A. Bharali and N. Singh, "Construction of Exactly Solvable Ring-Shaped Potentials," Journal of Modern Physics, Vol. 4 No. 4, 2013, pp. 463-467. doi: 10.4236/jmp.2013.44065.

Conflicts of Interest

The authors declare no conflicts of interest.


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