CLASSICAL AND NONCLASSICAL EIGENVALUE ASYMPTOTICS FOR MAGNETIC SCHRODINGER-OPERATORS

In this paper we consider Schrödinger operators with magnetic fields and study which of the magnetic field and the scalar potential contributes to the leading term of the asymptotic distribution of eigenvalues. By studying the asymptotic behavior of the trace of the heat kernels, we see that, if the norm of the magnetic field diverges at infinity faster than the scalar potential, only the magnetic field contributes to the leading asymptotic and that only the scalar potential does if the opposite under mild conditions. © 1991.