AN EXACT SOLUTION OF THE DIRAC OSCILLATOR PROBLEM IN THE CONTEXT OF GENERALIZED UNCERTAINTY PRINCIPLE

Md. Arifuzzaman, Md. Moniruzzaman,S. B. Faruque

Abstract: In this paper, we present an exact solution of the Dirac oscillator problem in one dimension in the context of the generalized uncertainty principle (GUP). The solution method presented here depends on the knowledge of the energy eigenvalues of the quantum harmonic oscillator with GUP. The crucial property of harmonic oscillator that the kinetic energy and the potential energy part of the Hamiltonian are of equal weight is used to obtain exact energy spectrum. Our result coincides with the results found in the literature. However, the solution procedure is completely different from others, very handy and alternative one. Moreover, we also remark the super symmetry aspects of the system.

Keywords: Dirac Oscillator; Generalized Uncertainty Principle; a Minimal Length.

DOI: https://doi.org/10.15623/ijret.2013.0209065