Time reversal symmetry in noncommutative phase space of the canonical type

Abstract

An algebra with noncommutativity of coordinates and noncommutativity of momenta which describes a rotationally- and time-reversal invariant quantum space is considered. A particle in a uniform field is studied in the space and the effect of space quantization on the energy levels of the particle is examined.
We find a perihelion shift of a particle in a Coulomb potential in noncommutative phase space. Upper bounds for the parameters of noncommutativity are estimated