 02140 M. Melgaard and G. Rozenblum
 Eigenvalue asymptotics for evendimensional perturbed Dirac
and Schr\"{o}dinger operators with constant magnetic fields
(129K, LaTeX 2e)
Mar 21, 02

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. The evendimensional Dirac and Schr\"{o}dinger operators
with a constant magnetic field have purely essential spectrum
consisting of isolated eigenvalues, socalled Landau levels.
For a signdefinite electric potential $V$ which tends to zero
at infinity, {\em not too fast}, it is known for the Schr\"{o}dinger
operator that the number of eigenvalues near each Landau level is
infinite and their leading (quasiclassical) asymptotics depends on
the rate of decay for $V$. We show, both for Schr\"{o}dinger and
Dirac operators, that, for {\em any} signdefinite, bounded $V$
which tends to zero at infinity, there still are an infinite number
of eigenvalues near each Landau level. For compactly supported $V$
we establish the {\em nonclassical} formula, not depending on $V$,
describing how the eigenvalues converge to the Landau levels
asymptotically.
 Files:
02140.src(
02140.keywords ,
manus1.tex )