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arXiv:hep-th/0210042 · The European Physical Journal C

Representations of non-commutative quantum mechanics and symmetries

Larisa Jonke, Stjepan Meljanac

Published Jul 1, 2003• 49 citations
arXivHTMLPDF
DOI
10.1140/epjc/s2003-01205-6

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The main point of this paper is to examine a “hidden” dynamical symmetry connected with the conservation of Laplace-Runge-Lenz vector (LRL) in the hydrogen atom problem solved by means of non-commutative quantum mechanics (NCQM). The basic features of NCQM will be introduced to the reader, the key one being the fact that the notion of a point, or a zero distance in the considered configuration space, is abandoned and replaced with a “fuzzy” structure in such a way that the rotational invariance is preserved. The main facts about the conservation of LRL vector in both classical and quantum theory will be reviewed. Finally, we will search for an analogy in the NCQM, provide our results and their comparison with the QM predictions. The key notions we are going to deal with are non-commutative space, Coulomb-Kepler problem, and symmetry.