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Extracting hidden symmetry from the energy spectrum

Yuzbashyan, EA and Happer, William and Altshuler, Boris L and Shastry, Sriram B (2003) Extracting hidden symmetry from the energy spectrum. In: Journal of Physics A Mathemetical and General, 36 (10). pp. 2577-2588.

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In this paper we revisit the problem of finding hidden symmetries in quantum mechanical systems. Our interest in this problem was renewed by nontrivial degeneracies of a simple spin Hamiltonian used to model spin relaxation in alkali-metal vapours. We consider this spin Hamiltonian in detail and use this example to outline a general approach to finding symmetries when eigenvalues and eigenstates of the Hamiltonian are known. We extract all nontrivial symmetries responsible for the degeneracy and show that the symmetry group of the Hamiltonian is SU(2). The symmetry operators have a simple meaning which becomes transparent in the limit of large spin. As an additional example we apply the method to the hydrogen atom.

Item Type: Journal Article
Publication: Journal of Physics A Mathemetical and General
Publisher: Institute of Physics
Additional Information: Copyright of this article belongs to Institute of Physics.
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Date Deposited: 19 Jul 2009 07:37
Last Modified: 05 Jul 2011 06:52
URI: http://eprints.iisc.ac.in/id/eprint/16930

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