Laplace-Runge-Lenz vector in quantum mechanics in noncommutative space

Abstract

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 noncommutative 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.

31 pages, 0 figures

References in corpus (1)

• The velocity operator in quantum mechanics in noncommutative space

Cited by in corpus (20)

• Quantum gauge theories on noncommutative 3-d space
• Noncommutative $R^d$ via closed star product
• Non-commutative deformation of Chern-Simons theory
• Poisson gauge theory
• A novel approach to non-commutative gauge theory
• $L_{\infty }$-Bootstrap Approach to Non-Commutative Gauge Theories
• Involutive representations of coordinate algebras and quantum spaces
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces
• Magnetic Monopoles in (Noncommutative) Quantum Mechanics
• Magnetic monopoles in noncommutative quantum mechanics
• On the physics of the $s{o}_q(4)$ hydrogen atom
• Computer Algebra in Physics: The hidden SO(4) symmetry of the hydrogen atom
• Alternative Description of Magnetic Monopoles in Quantum Mechanics
• NC plane waves, Casimir effect and flux tube potential with Lüscher terms
• Magnetic monopoles and symmetries in noncommutative space
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness
• Four-dimensional noncommutative deformations of $U(1)$ gauge theory and $L_{\infty }$ bootstrap
• Fradkin-Bacry-Ruegg-Souriau vector in kappa-deformed space-time
• Quantum Mechanics in Noncommutative space