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Supersymmetry approaches to the radial bound states of the hydrogen‐like atoms
Author(s) -
Chenaghlou A.,
Fakhri H.
Publication year - 2004
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.20276
Subject(s) - supersymmetry , hydrogen atom , bound state , generalization , factorization , physics , bessel function , supersymmetric quantum mechanics , quantum mechanics , product (mathematics) , quantum number , mathematical physics , upper and lower bounds , quantum , mathematics , quantum statistical mechanics , mathematical analysis , geometry , algorithm , group (periodic table)
Introducing the associated Bessel polynomials in terms of two non‐negative integers, we factorize their corresponding differential equation into a product of first‐order differential operators by four different ways as shape invariance equations. Then, the radial part of the bound states of the Schrödinger equation of a hydrogen‐like atom is derived using one of the factorization methods in the framework of supersymmetric quantum mechanics. In this approach, we regenerate the radial bound states and their corresponding spectrum, which are consistent with the well‐known facts. Based on the generalization of the supersymmetry idea, we shall show that two hydrogen‐like atoms with the same energy of the electron possess three extra supersymmetric structures in addition to an ordinary one. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005