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Construction of Exactly Solvable Ring-Shaped Potentials
Bajali College, Pathsala-781325, Assam, India
Department of Physics, Gauhati University, Guwahati-781014, Assam, India
- 1 Bajali College, Pathsala-781325, Assam, India
- 2 Department of Physics, Gauhati University, Guwahati-781014, Assam, India
Journal of Modern Physics·Volume 04 (2013)·Pages 463–467·Published 19 April 2013·DOI10.4236/jmp.2013.44065
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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.
KeywordsSchrödinger EquationExtended TransformationSpecial FunctionRing-Shaped PotentialNormalization
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