IJPAM: Volume 10, No. 3 (2004)

SEMICLASSICAL ASYMPTOTICS OF EIGENVALUES
FOR THE DIRAC OPERATOR WITH MAGNETIC
AND ELECTRIC POTENTIALS

Junichi Aramaki
Department of Mathematical Sciences
School of Science and Engineering
Tokyo Denki University
Hatoyama-Machi, Hiki-Gun
Saitama-Ken 350-0394, JAPAN
e-mail: aramaki@r.dendai.ac.jp


Abstract.We consider the Dirac operator with magnetic and electric potentials. Our final aim is to get the asymptotic behavior of the eigenvalues in the semiclassical sense. In the particular case of single well, we get a sufficient condition for the eigenvalue to be non-degenerate and then we can give the asymptotic expansion of the eigenvalue. We also give an example which seems to be new.

Received: November 11, 2003

AMS Subject Classification: 35Q60, 47F05

Key Words and Phrases: Dirac operator, semiclassical analysis, eigenvalue asymptotics

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 10
Issue: 3