Physics – Quantum Physics
Scientific paper
2012-02-29
Physics
Quantum Physics
7 pages, RevTeX4. A discussion on the N=1 case has been added with the boundary condition properly treated
Scientific paper
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.
Draayer Jerry P.
Liu Yi-Bin
Pan Feng
Shi Chang-Liang
Xie Ming-Xia
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