Lamb shift and Stark effect in simultaneous space-space and momentum-momentum noncommutative quantum mechanics and $\theta$-deformed $su(2)$ algebra

TL;DR

This paper investigates the effects of simultaneous space-space and momentum-momentum noncommutativity on the hydrogen atom's spectrum, including Lamb shift and Stark effect, introducing a $ heta$-deformed $su(2)$ algebra.

Contribution

It introduces a $ heta$-deformed $su(2)$ algebra and analyzes spectral shifts in hydrogen due to noncommutativity effects.

Findings

Lamb shift widths are larger with noncommutativity.

Spectral shifts depend on noncommutative parameters.

New algebraic structures for identical particles in noncommutative space.

Abstract

We study the spectrum of Hydrogen atom, Lamb shift and Stark effect in the framework of simultaneous space-space and momentum-momentum (s-s, p-p) noncommutative quantum mechanics. The results show that the widths of Lamb shift due to noncommutativity is bigger than the one presented in [1]. We also study the algebras of abservables of systems of identical particles in s-s, p-p noncommutative quantum mechanics. We intoduce $\theta$-deformed $su(2)$ algebra.