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Quasi-exactly Solvable Cases of the N-Dimensional Symmetric Quartic Anharmonic Oscillator |
| PAN Feng1,2, XIE Ming-Xia1, SHI Chang-Liang1, J. P. DRAAYER2 |
1Department of Physics, Liaoning Normal University, Dalian 116029
2Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA |
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| Cite this article: |
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PAN Feng, XIE Ming-Xia, SHI Chang-Liang et al 2012 Chin. Phys. Lett. 29 070304 |
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Abstract The O(N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions. The problem is directly related to that of a quantum double well anharmonic oscillator in an external field. A finite dimensional matrix equation for the problem is constructed explicitly, along with analytical expressions for some excited states in the system. The corresponding Niven equations for determining the polynomial solutions for the problem are given.
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Received: 11 April 2012
Published: 29 July 2012
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| PACS: |
03.65.Ge
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(Solutions of wave equations: bound states)
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02.30.Mv
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(Approximations and expansions)
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02.20.Qs
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(General properties, structure, and representation of Lie groups)
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02.60.Lj
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(Ordinary and partial differential equations; boundary value problems)
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