Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential

Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential

We study the generalized quantum isotonic oscillator Hamiltonian given by H=−d2/dr2+l(l+1)/r2+w2r2+2g(r2−a2)/(r2+a2)2, g>0. Two approaches are explored. A method for finding the quasipolynomial solutions is presented, and explicit expressions for these polynomials are given, along with the condit...

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Main Authors: Nasser Saad, Richard L. Hall, Hakan Çiftçi, Özlem Yeşiltaş
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2011/750168
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spelling doaj-543e6bacfddc496b9c2b0ba2cb063cfb2021-07-02T02:04:01ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392011-01-01201110.1155/2011/750168750168Study of the Generalized Quantum Isotonic Nonlinear Oscillator PotentialNasser Saad0Richard L. Hall1Hakan Çiftçi2Özlem Yeşiltaş3Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Avenue, Charlottetown, PE, C1A 4P3, CanadaDepartment of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montréal, QC, H3G 1M8, CanadaDepartment of Physics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara, TurkeyDepartment of Physics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara, TurkeyWe study the generalized quantum isotonic oscillator Hamiltonian given by H=−d2/dr2+l(l+1)/r2+w2r2+2g(r2−a2)/(r2+a2)2, g>0. Two approaches are explored. A method for finding the quasipolynomial solutions is presented, and explicit expressions for these polynomials are given, along with the conditions on the potential parameters. By using the asymptotic iteration method, we show how the eigenvalues of this Hamiltonian for arbitrary values of the parameters g, w, and a may be found to high accuracy.http://dx.doi.org/10.1155/2011/750168
collection DOAJ
language English
format Article
sources DOAJ
author Nasser Saad
Richard L. Hall
Hakan Çiftçi
Özlem Yeşiltaş
spellingShingle Nasser Saad
Richard L. Hall
Hakan Çiftçi
Özlem Yeşiltaş
Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential
Advances in Mathematical Physics
author_facet Nasser Saad
Richard L. Hall
Hakan Çiftçi
Özlem Yeşiltaş
author_sort Nasser Saad
title Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential
title_short Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential
title_full Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential
title_fullStr Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential
title_full_unstemmed Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential
title_sort study of the generalized quantum isotonic nonlinear oscillator potential
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2011-01-01
description We study the generalized quantum isotonic oscillator Hamiltonian given by H=−d2/dr2+l(l+1)/r2+w2r2+2g(r2−a2)/(r2+a2)2, g>0. Two approaches are explored. A method for finding the quasipolynomial solutions is presented, and explicit expressions for these polynomials are given, along with the conditions on the potential parameters. By using the asymptotic iteration method, we show how the eigenvalues of this Hamiltonian for arbitrary values of the parameters g, w, and a may be found to high accuracy.
url http://dx.doi.org/10.1155/2011/750168
work_keys_str_mv AT nassersaad studyofthegeneralizedquantumisotonicnonlinearoscillatorpotential
AT richardlhall studyofthegeneralizedquantumisotonicnonlinearoscillatorpotential
AT hakanciftci studyofthegeneralizedquantumisotonicnonlinearoscillatorpotential
AT ozlemyesiltas studyofthegeneralizedquantumisotonicnonlinearoscillatorpotential
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