Resonances of the Square Root of the Pauli Operator

Abstract

We investigate the spectral properties of two relativistic Hamiltonians: one is the square root of a Pauli operator with an electric potential growing polynomially at infinity, and the other differs from it only in the sign of the potential. Moreover, we show that resonances (eigenvalues) of each of them converge to resonances (eigenvalues) of the corresponding Pauli operators with the same potential in the nonrelativistic limit.