Effects of magnetic field on the evolution of the wave function of a charged particle with an angular momentum

We have calculated the effect of a magnetic field on the evolution of angular momentum eigenfunctions of a charged particle. An additional harmonic potential is supplemented to trap the wave packet. We find the probability density of the wave function is oscillating in the radial direction with a time period determined by the strength of the effective harmonic potential. When the magnetic field is along the z direction, if the initial wave function is an eigenfunction of (L) over cap (z), the probability density of the particle remains axis-symmetric. While for the case of an eigenfunction of (L) over cap (x), it is anisotropic in the x-y plane and rotates with a time period inverse proportional to the strength of the external magnetic field. We also extend the results in a phenomenological way to the case with an external magnetic field that varies harmonically in time.