Hydrogen and exotic atoms in rotationally-invariant space with noncommutativity of coordinates and noncommutativity of momenta

Abstract

The effect of the noncommutativity of coordinates and noncommutativity of momenta on the spectrum of the hydrogen atom is studied. Corrections to the energy levels of the atom up to the second order in the parameter of noncommutativity are found. Based on the obtained results and the experimental data for the 1S-2S transition frequency, the upper bound for the minimal length is obtained. Also, a two-particle system with Coulomb interaction is examined and hydrogen-like exotic atoms are studied in rotationally-invariant noncommutative phase space.