An exact solution to the Dirac equation for a time dependent Hamiltonian in 1-1D space-time

TL;DR

This paper presents an exact analytical solution to the Dirac equation in one spatial and one temporal dimension with a complex, time-dependent potential combining electric, scalar, and pseudoscalar components.

Contribution

The work provides a novel exact solution to the Dirac equation under a multi-component, time-dependent potential in 1+1D space-time, expanding analytical methods in relativistic quantum mechanics.

Findings

Exact solution derived for the Dirac equation with complex time-dependent potential.

Demonstrates the solvability of the Dirac equation in non-static, multi-component potential scenarios.

Enhances understanding of relativistic particles in dynamic fields.

Abstract

We find an exact solution to the Dirac equation in 1-1 dimensional space-time in the presence of a time-dependent potential which consists of a combination of electric, scalar, and pseudoscalar terms.