Runge-Lenz vector, accidental SU(2) symmetry, and unusual multiplets for motion on a cone

Journal Article · Tue Jan 15 00:00:00 EST 2008 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2007.08.004· OSTI ID:21077676

Wiese, U -J ^[1]

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1. Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland)

We consider a particle moving on a cone and bound to its tip by 1/r or harmonic oscillator potentials. When the deficit angle of the cone divided by 2{pi} is a rational number, all bound classical orbits are closed. Correspondingly, the quantum system has accidental degeneracies in the discrete energy spectrum. An accidental SU(2) symmetry is generated by the rotations around the tip of the cone as well as by a Runge-Lenz vector. Remarkably, some of the corresponding multiplets have fractional 'spin' and unusual degeneracies.

• OSTI ID: 21077676
• Journal Information: Annals of Physics (New York), Vol. 323, Issue 1; Other Information: DOI: 10.1016/j.aop.2007.08.004; PII: S0003-4916(07)00122-4; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CONES
ENERGY SPECTRA
HARMONIC OSCILLATORS
MULTIPLETS
ORBITS
POTENTIALS
QUANTUM MECHANICS
ROTATION
SPIN
SU-2 GROUPS
SYMMETRY
VECTORS