Asymptotic Distribution of Negative Eigenvalues for Three Dimensional Pauli Operators with Nonconstant Magnetic Fields

Abstract

We study the asymptotic distribution of negative eigenvalues of three dimensional Pauli operators with a two dimensional magnetic field and a three dimensional potential which decay to zero at infinity. For $\lambda >0$ suffciently small, we estimate the number of eigenvalues less than $-\lambda$ of such Pauli operators.