Yuzbashyan, A. ; Happer, William ; Altshuler, Boris L. ; Shastry, Sriram B. (2003) Extracting hidden symmetry from the energy spectrum Journal of Physics A: Mathematical and General, 36 (10). pp. 2577-2588. ISSN 0305-4470
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Official URL: http://iopscience.iop.org/0305-4470/36/10/317
Related URL: http://dx.doi.org/10.1088/0305-4470/36/10/317
Abstract
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: | Article |
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Source: | Copyright of this article belongs to Institute of Physics. |
ID Code: | 50795 |
Deposited On: | 26 Jul 2011 12:37 |
Last Modified: | 18 May 2016 04:57 |
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