Cwikel-Lieb-Rozenblum type estimates for the Pauli and magnetic Schr\"odinger operator in dimension two

Abstract

We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of Pauli operators in dimension two. The resulting upper bound is sharp both in the weak as well as in the strong coupling limit. We also derive different upper bounds for magnetic Schr\"odinger operators. The nature of the two estimates depends on whether or not the spin-orbit coupling is taken into account.