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.
Highlights
Moshinsky and Szczepaniak [1] have introduced an interesting interaction in the Dirac equation such that the Dirac Hamiltonian is linear in both momentum and the coordinates
The system is cylindrically symmetric: there are basically two oscillators, one is a 2D oscillator in the x-y plane and the other is a 1D oscillator in the z - direction
There is spin-orbit coupling coupled with the Dirac oscillator in the third term in Eqs. (36) and (39) or (49) and (50)
Summary
Moshinsky and Szczepaniak [1] have introduced an interesting interaction in the Dirac equation such that the Dirac Hamiltonian is linear in both momentum and the coordinates. The resulting Dirac equation is known as Dirac oscillator because it turns into a harmonic oscillator with strong spin-orbit coupling in the non-relativistic limit. A tabletop implementation of a Dirac oscillator system based on a spin-orbit coupled ultracold atomic sample that allows for a direct observation of the corresponding analog of virtual pair creation on quantum measurement backaction has been proposed [19]. The propagator of a two dimensional Dirac oscillator in the presence of a uniform electric field is derived by a path integral technic [20]. Dimensional harmonic oscillator with a spin-orbit and contribution, when the magnetic field is absent.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
