Relativistic Hamiltonians with dilation analytic potentials diverging at infinity

Abstract

We investigate the spectral properties of the Dirac operator with a potential V(x) and two relativistic Schrödinger operators with V(x) and -V(x), respectively. The potential V(x) is assumed to be dilation analytic and diverge at infinity. Our approach is based on an abstract theorem related to dilation analytic methods, and our results on the Dirac operator are obtained by analyzing dilated relativistic Schrödinger operators. Moreover, we explain some relationships of spectra and resonances between Schrödinger operators and the Dirac operator as the nonrelativistic limit.