Superintegrability of the Caged Anisotropic Oscillator

Details Superintegrability of the Caged Anisotropic Oscillator Superintegrability of the Caged Anisotropic Oscillator

2008-08-15

arxiv.org/abs/0808.2146v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Submitted to the Journal of Mathematical Physics

Scientific paper

10.1063/1.2988133

We study "the Caged Anisotropic Harmonic Oscillator", which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n), but additionally with barrier terms describing repulsive forces from the principal planes. This confines the classical motion to a sector bounded by the principal planes, or cage. In 3 degrees, there are five isolating integrals of motion, ensuring that all bound trajectories are closed and strictly periodic. Three of the integrals are quadratic in the momenta, the remaining two are polynomials of order 2(l+m-1) and 2(l+n-1). In the quantum problem, the eigenstates are multiply degenerate, exhibiting multiple copies of the fundamental pattern of the symmetry group SU(3).

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