Extracting Hidden Symmetry from the Energy Spectrum
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 vapors. 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.
Keywords
Cite
@article{arxiv.cond-mat/0210506,
title = {Extracting Hidden Symmetry from the Energy Spectrum},
author = {Emil A. Yuzbashyan and William Happer and Boris L. Altshuler and B. Sriram Shastry},
journal= {arXiv preprint arXiv:cond-mat/0210506},
year = {2009}
}
Comments
14 pages, 1 figure. A minor typo corrected