Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space-time

TL;DR

This paper investigates how non-inertial rotating frames and non-commutative geometry influence the energy spectrum of a Dirac oscillator in a cosmic string space-time, revealing complex bound-state solutions and scaling behaviors.

Contribution

It introduces a novel analysis of the Dirac oscillator under combined non-inertial and non-commutative effects in a cosmic string background, providing approximate solutions and energy scaling insights.

Findings

Bound-state solutions relate to biconfluent Heun polynomials.

Fundamental state energy is obtained analytically with a hard-wall condition.

Ground-state energy scales with non-commutative and physical parameters.

Abstract

We examine the non-inertial effects of a rotating frame on a Dirac oscillator in a cosmic string space-time with non-commutative geometry in phase space. We observe that the approximate bound-state solutions are related to the biconfluent Heun polynomials. The related energies cannot be obtained in a closed form for all the bound states. We find the energy of the fundamental state analytically by taking into account the hard-wall confining condition. We describe how the ground-state energy scales with the new non-commutative term as well as with the other physical parameters of the system.