Two-particle system in noncommutative space with preserved rotational symmetry

TL;DR

This paper investigates a two-particle system in a rotationally invariant noncommutative space, deriving effective noncommutative algebra for center-of-mass and relative coordinates, and calculates energy level corrections for the hydrogen atom.

Contribution

It introduces a model of a two-particle system in noncommutative space that preserves rotational symmetry and computes energy corrections for hydrogen.

Findings

Effective noncommutative algebra for center-of-mass and relative coordinates.

Second-order energy corrections for hydrogen atom.

Preservation of rotational symmetry in noncommutative space.

Abstract

We consider a system of two particles in noncommutative space which is rotationally invariant. It is shown that the coordinates of the center-of-mass position and the coordinates of relative motion satisfy noncommutative algebra with corresponding effective tensors of noncommutativity. The hydrogen atom is studied as a two-particle system. We find the corrections to the energy levels of the hydrogen atom up to the second order over the parameter of noncommutativity.