The Dirac Equation in (1+2)-dimensional G\"{u}rses space-time backgrounds

TL;DR

This paper explores the behavior of spin-1/2 particles in a (1+2)-dimensional G"{u}rses spacetime, solving the Dirac equation to understand how the background affects quantum dynamics and energy levels.

Contribution

It provides an exact solution to the Dirac equation in G"{u}rses spacetime using the Nikiforov-Uvarov method, revealing the influence of the background geometry on eigenvalues.

Findings

Derived explicit energy eigenvalues

Obtained wave functions for particles in G"{u}rses space-time

Analyzed effects of spacetime curvature on quantum states

Abstract

In this article, we investigate the relativistic quantum dynamics of spin-$\frac{1}{2}$ particles in (1+2)-dimensional G\"{u}rses space-time backgrounds, and analyze the effects on the eigenvalues. We solve the Dirac equation using the Nikiforov-Uvarov method in the considered framework, and evaluate the energy eigenvalues and corresponding wave function.