Runge-Lenz vector, accidental SU(2) symmetry, and unusual multiplets for motion on a cone |
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Authors: | MH Al-Hashimi U-J Wiese |
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Institution: | Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern, Switzerland |
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Abstract: | 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 2π 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. |
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Keywords: | Accidental symmetry Quantum mechanics Motion on a cone SU(2) algebra and unusual multiplets Fractional spin Self-adjoint extension |
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