On the Dirac Oscillator

Abstract

In the present work we obtain a new representation for the Dirac oscillator based on the Clifford algebra $C{\ell }_7.$ The symmetry breaking and the energy eigenvalues for our model of the Dirac oscillator are studied in the non-relativistic limit.

10 pages, no figure. News references and comments. This work begun in collaboration with Jambunatha Jayaraman (In memory) and Arvind Narayan Vaidya (In memory), author's Ph. D. supervisors, whose advises and encouragement were fundamental in the development of the thesis. To appear in Physics Letters A

References in corpus (7)

• Pseudospin symmetry and the relativistic harmonic oscillator
• Dirac oscillator with nonzero minimal uncertainty in position
• Relativistic Harmonic Oscillator with Spin Symmetry
• One-dimensional Dirac oscillator in a thermal bath
• Exact solution of the two-dimensional Dirac oscillator
• Relativistic quantum mechanics of a Dirac oscillator
• The Dirac-Oscillator Green's function

Cited by in corpus (11)

• The Dirac oscillator in a spinning cosmic string spacetime
• Dirac oscillator in an external magnetic field
• Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background
• Exact Solution of the Relativistic Dunkl Oscillator in $(2+1)$ Dimensions
• Noncommutative Dirac oscillator in an external magnetic field
• The DKP oscillator with a linear interaction in the cosmic string space-time
• Algebraic approach for the one-dimensional Dirac-Dunkl oscillator
• Coherent states for the two-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field
• First and second-order relativistic corrections to the two and higher-dimensional isotropic harmonic oscillator obeying the spinless Salpeter equation
• Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions
• Canonical quantization of the Dirac oscillator field in (1+1) and (3+1) dimensions