The One-dimensional Box Problem and the Dirac Oscillator in R-Minkowski Spacetime

Abstract

In this paper, we establish some of the deformed calculus for R-Minkowski space-time. We start by defining the deformed derivative in R-Minkowski spacetime, the deformed exponential and trigonometric functions, deformed Fourier transform and its inverse transformation, and then we apply all that to the study of the one-dimensional box problem in a position representation. Thereafter, we study the one-dimensional Dirac harmonic oscillator, and as a consequence we obtain the energy spectrum of the latter in R-Minkowski space-time.