Novel energy level structure of Dirac oscillator in magnetic field

TL;DR

This paper provides a comprehensive solution to the Dirac oscillator in a magnetic field, revealing a complex energy spectrum with novel couplings between oscillator, Larmor, spin, and orbital motions.

Contribution

It presents the full solution and energy spectrum of the Dirac oscillator under axial magnetic field, highlighting new coupling effects and spectral structures.

Findings

Rich and novel energy spectrum with coupling of oscillator and Larmor frequencies

Coupling between spin and orbital motion observed

Energy levels show complex interactions influenced by magnetic field

Abstract

We have presented an elegant high energy quantum problem, namely, the full Dirac oscillator under axial magnetic field with its full solution. We have found the energy spectrum which is rich and at the same time has a novel structure. The quantized energy levels show coupling of the oscillator frequency with the Larmor frequency in the 2D surface where the electrons under consideration follow a 2D oscillator. The axis in which magnetic field is pointed, the electrons follow a 1D oscillator. There is also coupling between spin and orbital motion and also a coupling between a resultant effect of orbital and spin motion with Larmor precession.