ANALYTICAL SOLUTION OF (2+1) DIMENSIONAL DIRAC EQUATION IN TIME-DEPENDENT NONCOMMUTATIVE PHASE-SPACE

Abstract

In this article, we studied the system of a (2+1) dimensional Dirac equation in a time-dependent noncommutative phase-space. More specifically, we investigated the analytical solution of the corresponding system by the Lewis-Riesenfeld invariant method based on the construction of the Lewis-Riesenfeld invariant. Knowing that we obtained the time-dependent Dirac Hamiltonian of the problem in question from a time-dependent Bopp-Shift translation, then used it to set the Lewis- Riesenfeld invariant operators. Thereafter, the obtained results were used to express the eigenfunctions that lead to determining the general solution of the system.

Keywords

• lewis-riesenfeld invariant method, time-dependent bopp-shift translation, bopp’s shift
• time-dependent dirac equation, time-dependent noncommutative phase-space