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Exactly solvable schrödinger equation for a class of multiparameter exponential‐type potentials
Author(s) -
GarcíaMartínez J.,
GarcíaRavelo J.,
Morales J.,
Peña J. J.
Publication year - 2012
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.23204
Subject(s) - isospectral , exponential type , exponential function , type (biology) , transformation (genetics) , hypergeometric function , mathematics , class (philosophy) , function (biology) , schrödinger equation , hypergeometric distribution , quantum , mathematical physics , mathematical analysis , pure mathematics , physics , quantum mechanics , chemistry , ecology , biochemistry , artificial intelligence , evolutionary biology , computer science , biology , gene
The solution to a spectral problem involving the Schrödinger equation for a particular class of multiparameter exponential‐type potentials is presented. The proposal is based on the canonical transformation method applied to a general second‐order differential equation, multiplied by a function g ( x ), to convert it into a Schrödinger‐like equation. The treatment of multiparameter exponential‐type potentials comes from the application of the transformed results to the hypergeometric equation under the assumption of a specific g ( x ). Besides presenting the explicit solutions and their spectral values, it is shown that the problem considered in this article unifies and generalizes several former studies. That is, the proposed exactly solvable multiparameter exponential‐type potential can be straightforwardly applied to particular exponential potentials depending on the choice of the involved parameters as exemplified for the Hulthén potential and their isospectral partner. Moreover, depending on the function g ( x ), the proposal can be extended to find different exactly solvable potentials as well as to generate new potentials that could be useful in quantum chemical calculations. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012