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
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
摘要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.
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.
(Ordinary and partial differential equations; boundary value problems)
引用本文:
PAN Feng, XIE Ming-Xia, SHI Chang-Liang, J. P. DRAAYER. Quasi-exactly Solvable Cases of the N-Dimensional Symmetric Quartic Anharmonic Oscillator[J]. 中国物理快报, 2012, 29(7): 70304-070304.
PAN Feng, XIE Ming-Xia, SHI Chang-Liang, J. P. DRAAYER. Quasi-exactly Solvable Cases of the N-Dimensional Symmetric Quartic Anharmonic Oscillator. Chin. Phys. Lett., 2012, 29(7): 70304-070304.
2012, Vol. 29 
