Quantum-mechanical description of charged particles with spin 1/2 in the magnetic field outside of a rectilinear current filament

The eigenstates of a charged particle with spin 1/2 in the magnetic field surrounding a rectilinear current filament are determined numerically. As they differ only slightly from local Landau levels, the wave functions may be approximated analytically using stationary perturbation theory. The expectation values of the component parallel to the wire of the velocity operator are calculated for both the exact and the approximated wave functions. They are a measure for the drift of the gyration center parallel to the wire, which is predicted by classical mechanics. Taking into account the quantization of the cyclotron rotation, this drift motion can also be derived by applying the method of adiabatic expansion of the particle propagator. The resulting values for the drift velocities are in excellent agreement with those from classical mechanics if, in the latter, one takes into account energy quantization. \textcopyright{} 1996 The American Physical Society.