On the contribution of the Coulomb singularity of arbitrary charge to the Dirac Hamiltonian
Author:
Jingbo Xia
Journal:
Trans. Amer. Math. Soc. 351 (1999), 19892023
MSC (1991):
Primary 47A10, 47F05, 81Q10, 81V45
Published electronically:
January 26, 1999
MathSciNet review:
1451618
Fulltext PDF Free Access
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Abstract: We study the selfadjoint extensions of the Dirac operator , where the electrical potential contains a Coulomb singularity of arbitrary charge and the magnetic potential is allowed to be unbounded at infinity. We show that if the Coulomb singularity has the form where has a limit at 0, then, for any selfadjoint extension of the Dirac operator, removing the singularity results in a HilbertSchmidt perturbation of its resolvent.
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Additional Information
Jingbo Xia
Affiliation:
Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14214
Email:
jxia@acsu.buffalo.edu
DOI:
http://dx.doi.org/10.1090/S000299479902084X
PII:
S 00029947(99)02084X
Keywords:
Dirac operator,
spectrum,
perturbation
Received by editor(s):
January 15, 1996
Received by editor(s) in revised form:
February 27, 1997
Published electronically:
January 26, 1999
Additional Notes:
Research supported in part by National Science Foundation grant DMS9400600.
Article copyright:
© Copyright 1999
American Mathematical Society
