Quantum mechanical E × B drift velocity in a weakly inhomogeneous electromagnetic field

Abstract

The analytical solution for the quantum mechanical drift velocity for a non-relativistic spinless charged particle of E × B drift in the presence of a weakly inhomogeneous electric and magnetic field for the magnetized plasma is presented. Using the Heisenberg equation of motion, the time evolution of the position and momentum operators for the charged particle is solved. From the time dependent operators, the analytical solution of the time dependent momenta operators and position operators is derived. The quantum mechanical expansion rates of variances are shown to agree with the numerical results. Most importantly, the quantum mechanical E × B drift velocity coincides perfectly with the classical drift velocity in the limit of Planck's constant being zero. With higher order electric field inhomogeneity, low energy particles would drift faster than what the classical drift theory predicts.