Eigenvalue estimates in the semi–classical limit for Pauli and Dirac operators with a magnetic field

Abstract

Leading–order semi–classical asymptotics are given for the distribution of the eigenvalues of Dirac and Pauli operators describing an electron in an electromagnetic field. Weak integrability conditions are assumed on the electric and magnetic potentials to ensure the existence of only a finite number of eigenvalues outside the essential spectra. The method used is based on coherent state analysis.