Superintegrability of the caged anisotropic oscillator

Journal Article · Mon Sep 15 04:00:00 EDT 2008 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2988133· OSTI ID:21175593

Evans, N W; Verrier, P E ^[1]

---

1. Institute of Astronomy, University of Cambridge, Madingley Rd., Cambridge CB3 0HA (United Kingdom)

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 a cage. In three degrees of freedom, 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 l{sup 2}m{sup 2}n{sup 2} copies of the fundamental pattern of the symmetry group SU(3)

• OSTI ID: 21175593
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 9 Vol. 49; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANISOTROPY
DEGREES OF FREEDOM
EIGENSTATES
HAMILTONIANS
HARMONIC OSCILLATORS
INTEGRAL EQUATIONS
INTEGRALS
PERIODICITY
POLYNOMIALS
QUANTUM MECHANICS
SU-3 GROUPS