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

Abstract

We have calculated the effect of 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 radial direction with a time period determined by the strength of the effective harmonic potential. When the magnetic field is along $z$ direction, if the initial wave function is eigenfunction of $\hat{L}_z$, the probability density of the particle remains axis symmetric. While for the case of eigenfunction of $\hat{L}_x$, 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.