Quantum mechanical grad-B drift velocity operator in a weakly non-uniform magnetic field

Abstract

This paper presents the analytical solution for quantum mechanical grad-B drift velocity operator by solving the Heisenberg equation of motion. Using the time dependent operators, it is shown the analytical solution of the position operators in x̂(t) and ŷ(t) of the particle in the presence of a weakly non-uniform magnetic field. It is also shown numerically that the grad-B drift velocity operator agrees with the classical counterpart.