Orbital magnetic moment of the electron in the hydrogen atom in deformed space with minimal length

TL;DR

This paper explores how a minimal length deformation in space affects the orbital magnetic moment of an electron in hydrogen, finding corrections comparable to relativistic effects but with an opposite sign, and estimating their upper bounds.

Contribution

It introduces a model of deformed space with minimal length and analyzes its impact on the electron's orbital magnetic moment in hydrogen.

Findings

Correction to magnetic moment depends on one deformation parameter.

The correction is similar to relativistic correction but with opposite sign.

Upper bound of correction is about 10^{-12}, below experimental error.

Abstract

We investigated the orbital magnetic moment of electron in the hydrogen atom in deformed space with minimal length. It turned out that corrections to the magnetic moment caused by deformation depend on one parameter in the presence of two-parametric deformation. It is interesting to note that the correction to orbital magnetic moment is similar to the correction that follows from relativistic theory but it has an opposite sign. Using the upper bound for minimal length obtained in previous papers we estimated the upper bound for relative correction to orbital magnetic moment and obtained the value $\sim 10^{-12}$. This is four power less than the relative error for most recent experimental values of Bohr magneton.