On the (2+1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty

TL;DR

This paper provides an exact solution to the (2+1)-dimensional Dirac equation in a magnetic field considering a minimal length, revealing a broader class of solutions than previously known.

Contribution

It introduces a novel method to solve the Dirac equation with minimal length, generalizing prior solutions and connecting them to even quantum numbers.

Findings

Exact solutions for the Dirac equation with minimal length

Generalization of previous solutions to include more quantum states

Identification of the previous solution as a subset of the new general solution

Abstract

We exactly solve the (2+1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two 2-dimensional non-relativistic harmonic oscillator and obtain the solutions without directly solving the corresponding differential equations which are presented by Menculini et al. [Phys. Rev. D 87, 065017 (2013)]. We also show that Menculini et al. solution is a subset of the general solution which is related to the even quantum numbers.