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

Author

Igarashi, H. ; Yoshikawa, T. ; Honma, T.

Author_Institution

Div. of Syst. & Inf. Eng., Hokkaido Univ., Sapporo, Japan

Volume

35

Issue

3

fYear

1999

fDate

5/1/1999 12:00:00 AM

Firstpage

1518

Lastpage

1521

Abstract

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

Keywords

Schrodinger equation; chaos; electromagnetic wave propagation; finite difference methods; magnetic fields; numerical stability; probability; quantum well devices; time-domain analysis; Trotter-Suzuki method; complex spatial patterns; explicit central difference scheme; finite difference method; magnetic field; numerical stability; probability density; quantum chaos; quantum well devices; rectangular-shaped domains; single electron dynamics; stadium-shaped domains; time-dependent Schrodinger equation; time-domain analysis; uniform magnetic field; wave packet motion; Chaos; Electrons; Finite difference methods; Legged locomotion; Magnetic analysis; Magnetic fields; Motion analysis; Numerical stability; Schrodinger equation; Time domain analysis;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/20.767256

Filename

767256