Hydrogen atom in rotationally invariant noncommutative space

TL;DR

This paper investigates the hydrogen atom within a rotationally invariant noncommutative space, calculating energy level corrections and estimating the noncommutativity parameter based on experimental spectral data.

Contribution

It introduces a rotationally invariant noncommutative algebra and derives second-order energy corrections for the hydrogen atom, providing bounds on noncommutativity from experimental results.

Findings

Energy levels receive second-order corrections due to noncommutativity.

An upper bound on the noncommutativity parameter is established.

Theoretical predictions are consistent with experimental spectral measurements.

Abstract

We consider the noncommutative algebra which is rotationally invariant. The hydrogen atom is studied in a rotationally invariant noncommutative space. We find the corrections to the energy levels of the hydrogen atom up to the second order in the parameter of noncommutativity. The upper bound of the parameter of noncommutativity is estimated on the basis of the experimental results for 1s-2s transition frequency.