Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring-type estimate

We give the leading order semiclassical asymptotics for the sum of the negative eigenvalues of the Pauli operator (in dimension two and three) with a strong non-homogeneous magnetic field. This result can be used to prove that the magnetic Thomas-Fermi theory gives the leading order ground state energy of large atoms. We develop a new localization scheme well suited to the anisotropic character of the strong magnetic field. We also use the basic Lieb-Thirring estimate obtained earlier (1996). (orig.) 19 refs.