Relativistic Hydrogen-Like Atom on a Noncommutative Phase Space

TL;DR

This paper investigates how noncommutative phase space modifies the energy levels of a relativistic hydrogen-like atom, revealing degeneracy removal and energy shifts due to noncommutative parameters.

Contribution

It introduces a modified Dirac Hamiltonian incorporating noncommutative parameters and calculates leading order corrections to specific energy levels.

Findings

Degeneracy of 2P_{1/2} and 2P_{3/2} levels is fully removed by heta-correction.

ar heta-correction causes shifts in energy levels.

Explicit corrections are derived for the energy levels in a noncommutative phase space.

Abstract

The energy levels of hydrogen-like atom on a noncommutative phase space were studied in the framework of relativistic quantum mechanics. The leading order corrections to energy levels 2S_{1/2}, 2P_{1/2} and 2P_{3/2} were obtained by using the \theta and the \bar\theta modified Dirac Hamiltonian of hydrogen-like atom on a noncommutative phase space. The degeneracy of the energy levels 2P_{1/2} and 2P_{3/2} were removed completely by \theta-correction. And the \bar\theta-correction shifts these energy levels.