Time-domain analysis of Schrodinger equation for single electron in magnetic field

In this paper the time-dependent Schrodinger equation governing dynamics of a single electron in magnetic fields is solved by the finite difference method (FDM) with the explicit central difference scheme and Trotter-Suzuki method (TSM). Motion of a wave packet in rectangular and stadium-shaped domains immersed in uniform magnetic field is analyzed. The performance of the two numerical methods is compared. It is shown that FDM is superior over TSM for accuracy and computing efficiency while TSM is superior for numerical stability. Moreover, the probability density of an electron in the stadium is shown to form complex spatial patterns which suggest quantum chaos.