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Exactly solvable quantum potentials with special functions solutions
Author(s) -
Peña J. J.,
Ovando G.,
Morales J.,
GarcíaRavelo J.,
García J.
Publication year - 2008
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.21611
Subject(s) - wave function , laguerre polynomials , quantum , hermite polynomials , transformation (genetics) , bessel function , special functions , mathematical physics , superpotential , physics , legendre function , legendre polynomials , quantum mechanics , mathematics , mathematical analysis , chemistry , supersymmetry , biochemistry , gene
In this work, a canonical point and a gauge transformation applied to the g ( x ) times differential equations (DE) for special functions (SF) is used to convert it into a Schrödinger‐like equation. This method leads to exactly solvable potentials allowing special functions solutions. For specific applications, keeping in mind the general DE for SF, the choice of the coefficients that identify the SF under study allows to find the equivalent of the Witten superpotential and wavefunctions for each g ( x ). That is, the choice of a particular g ( x ) leads straightforwardly to those exactly solvable potentials having as wavefunctions the SF under consideration. As a useful application of the proposed method, we considered explicitly the potentials associated to the standard Hermite, Laguerre, Legendre, and Bessel SF in the case of some particular forms of g ( x ). However, the proposed approach can be directly applied to any other standard SF with the aim to obtain exactly solvable potentials that can be used in the modelling of quantum chemical applications. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008