Scattering of an electron by a two-dimensional parabolic potential and a perpendicular magnetic field

A formula providing the charge distribution of an electron under the influence of a two-dimensional parabolic potential and a perpendicular to its plane constant magnetic field via the evolving wave function stemming from a wave packet locating the particle at a certain position in the potential plane and carrying an initial momentum. There follows a picture of the evolving charge distribution. In particular, the motion of the top maximum is derived in the course of time. The distribution begins with a high peak in the vicinity of the wave packet center followed by spread in the form of a wave extending around a rotating radius in the plane of the potential and emanating from its origin. As time goes by the charge distribution peak reappears in its original form at equal distance from the potential origin after traversing an angle depending on the system's initial position and frequency characteristics of the prevailing force field. The process of charge distribution concentration followed by smearing is repeated at equal time intervals relating to a combination of frequencies associated with the field of force.