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: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2011/750168 |
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| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |