M. Melgaard and G. Rozenblum
Eigenvalue asymptotics for even-dimensional perturbed Dirac 
and Schr\"{o}dinger operators with constant magnetic fields
(129K, LaTeX 2e)

ABSTRACT.  The even-dimensional Dirac and Schr\"{o}dinger operators 
with a constant magnetic field have purely essential spectrum 
consisting of isolated eigenvalues, so-called Landau levels. 
For a sign-definite 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 (quasi-classical) asymptotics depends on 
the rate of decay for $V$. We show, both for Schr\"{o}dinger and 
Dirac operators, that, for {\em any} sign-definite, 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 non-classical} formula, not depending on $V$, 
describing how the eigenvalues converge to the Landau levels 
asymptotically.