The exact solution of the Dirac equation with a static magnetic field under the influence of the generalized uncertainty principle

Abstract

We present an exact solution of the Dirac equation with a static magnetic field in the context of the generalized uncertainty principle (GUP). The procedure for finding the solution of the problem depends on the knowledge of the energy spectrum of the harmonic oscillator with the GUP and the property of the harmonic oscillator that the kinetic and potential energy parts of the Hamiltonian are of equal weight. The exact solution of the Dirac equation thus obtained describes electrons in the presence of a uniform magnetic field and in the scenario of the GUP.