A novel finite-element formulation for the analysis of the energy levels of a quantum cavity in a magnetic field

Author

Hirayama, Koichi ; Honma, Yasuhiro ; Hayashi, Yoshio ; Koshiba, Masanori

Author_Institution

Dept. of Electr. & Electron. Eng., Kitami Inst. of Technol., Japan

Volume

10

Issue

10

fYear

1998

Firstpage

1359

Lastpage

1361

Abstract

A novel finite-element formulation for the analysis of the energy levels of a two-dimensional quantum cavity in a magnetic field is proposed. Our formulation is based on both a variational and Galerkin methods which, when combined with a finite-element method, lead to eigenvalue problems characterized by either real or Hermitian matrices contrary to algorithms proposed in the past. These eigenvalue problems can then be solved quite efficiently on a computer using standard library packages. Also, it is confirmed that the results obtained here are independent of the choice of gauge.

Keywords

Galerkin method; Hermitian matrices; eigenvalues and eigenfunctions; finite element analysis; magneto-optical effects; optical resonators; quantum optics; Galerkin methods; Hermitian matrices; eigenvalue problems; energy level analysis; finite-element formulation; finite-element method; magnetic field; quantum cavity; standard library packages; two-dimensional quantum cavity; variational methods; Eigenvalues and eigenfunctions; Electrons; Energy states; Finite element methods; Magnetic analysis; Magnetic fields; Moment methods; Sparse matrices; Symmetric matrices; Transmission line matrix methods;

fLanguage

English

Journal_Title

Photonics Technology Letters, IEEE

Publisher

ieee

ISSN

1041-1135

Type

jour

DOI

10.1109/68.720260

Filename

720260