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

Ilyas Haouam

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

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague