Dirac Particle in Crossed Electric and Magnetic Field


  • B. A. Kagali Department of Physics, Bangalore University, Bengaluru, India-560056
  • T. Shivalingaswamy P.G. Department of Physics, Maharani’s Science College for Women (Autonomous), Mysore, India-570005
  • Felan Amal St. Philomena,s College (Autonomous), Mysore




Bound States, Crossed Electric and Magnetic Fields, Landau Levels, Dirac Equation, Landau Gauge


Electromagnetic forces play a critical role in shaping the trajectories of charged particles, affecting their movement
across scales ranging from subatomic dimensions to distances smaller than astronomical ones. This study focuses
on the behaviour of a charged spin-half particle exposed to a perpendicular electric and magnetic field. We analyze the associated eigenfunctions and eigenvalues using the Landau gauge. The non-relativistic and classical limits align with the standard results.


John David Jackson. Classical electrodynamics; 2nd ed. Wiley, New York, NY, 1975.

L. D. Landau and E. M. Lifshitz. The Classical Theory of Fields; 3rd ed. Pergamon Press, New York, 1971.

D.J. Griffiths. Introduction to Electrodynamics. Pearson Education, 2014.

S. Glasstone and R.H. Lovberg. Controlled Thermonuclear Reactions: An Introduction to Theory and Experiment. Van Nostrand, 1960.

B. Barbashov and A. Pestov. Solution of the problem of charge motion in crossed electric and magnetic fields. Theoretical and Mathematical Physics, 186:440–446, 03 2016.

B.A. Kagali and T Shivalingaswamy. Quantum states of a relativistic charged particle in crossed electric and magnetic fields. Mapana-Journal of Sciences, 20(3):43–48, 2021.

R. Shankar. Plenum Press, New York, NY, 1994.

Additional Files