Dynamical Symmetry of the Zwanziger problem in Non-commutative Quantum Mechanics

Abstract

The non-relativistic hydrogen atom and the Zwanziger problem have the same dynamical symmetry for bound and scattering states.We show that this is also true for a Hilbert space which is non-commutative in co-ordinates. The group structure is described using the redefined velocity operator and Laplace Runge-Lenz operator in terms of left and right handed representations of the non-commutative Hilbert space $R_{\lambda }^3$.The bound state algebra is SO(4) and the scattering state algebra is SO(3,1).

9 pages, work in review at (journal) Physics Education- Indian Association of Physics Teachers Manuscript number-PE14-12-276

References in corpus (2)

• Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
• Coulomb problem in NC quantum mechanics: Exact solution and non-perturbative aspects