Analytical Solution of (2+1) Dimensional Dirac Equation in Time-Dependent Noncommutative Phase-Space

TL;DR

This paper derives an exact analytical solution for the (2+1) dimensional Dirac equation in a time-dependent noncommutative phase-space using the Lewis-Riesenfeld invariant method, advancing understanding of quantum systems in noncommutative geometries.

Contribution

It presents the first analytical solution of the Dirac equation in a time-dependent noncommutative phase-space using the Lewis-Riesenfeld invariant approach.

Findings

Derived the time-dependent Dirac Hamiltonian via Bopp-Shift translation.

Constructed Lewis-Riesenfeld invariant operators for the system.

Obtained explicit eigenfunctions and general solutions of the Dirac equation.

Abstract

In this article, we studied the system of (2+1) dimensional Dirac equation in time-dependent noncommutative phase-space. Exactly, 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 it used to set the Lewis-Riesenfeld invariant operators. Thereafter, the obtained results used to express the eigenfunctions that lead to determining the general solution of the system.