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Degeneracy of confined D ‐dimensional harmonic oscillator
Author(s) -
Montgomery H. E.,
Aquino N. A.,
Sen K. D.
Publication year - 2006
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.21211
Subject(s) - degeneracy (biology) , eigenvalues and eigenvectors , harmonic oscillator , hypergeometric function , isotropy , quantum mechanics , physics , harmonic , hamiltonian (control theory) , radius , hypergeometric distribution , mathematical physics , quantum , mathematics , mathematical analysis , pure mathematics , bioinformatics , mathematical optimization , computer security , computer science , biology
Using the mathematical properties of the confluent hypergeometric functions, the conditions for the incidental, simultaneous, and interdimensional degeneracy of the confined D ‐dimensional ( D > 1) harmonic oscillator energy levels are derived, assuming that the isotropic confinement is defined by an infinite potential well and a finite radius R c . Very accurate energy eigenvalues are obtained numerically by finding the roots of the confluent hypergeometric functions that confirm the degeneracy conditions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007