# Noncommutative phase space with rotational symmetry and hydrogen atom

## TL;DR

This paper develops a rotationally invariant noncommutative phase space algebra and investigates its effects on hydrogen atom energy levels, providing bounds on noncommutativity parameters.

## Contribution

It introduces a new algebra for noncommutative phase space that preserves rotational symmetry and analyzes its impact on hydrogen atom spectra.

## Key findings

- Corrections to energy levels up to second order in noncommutativity parameters.
- Estimated upper bounds for noncommutativity parameters.
- Demonstrated rotational invariance of the noncommutative algebra.

## Abstract

We construct algebra with noncommutativity of coordinates and noncommutativity of momenta which is rotationally invariant and equivalent to noncommutative algebra of canonical type. Influence of noncommutativity on the energy levels of hydrogen atom is studied in rotationally invariant noncommutative phase space. We find corrections to the levels up to the second order in the parameters of noncommutativity and estimate the upper bounds of these parameters.