Lewis-Riesenfeld Approach to the Solution of the Dirac Equation in Time-Dependent Non-Commutative Phase Space

Abstract

In this paper we investigated the solution of the Dirac equation in the time dependent non commutative phase-space using the Lewis–Riesenfeld invariant method. Wherein the Dirac time dependent hamiltonian obtained from a time dependent Bopp-Shift linear translation, then it used to construct the Lewis–Riesenfeld invariant operators. Afterward the results are used to obtain the general solution of the system.