Spectral Properties of Schrödinger Operators with Irregular Magnetic Potentials, for a Spin 12 Particle

AbstractThe two-dimensional Schrödinger operatorH̃(a) for a spin 12 particle is considered. The magnetic fieldbgenerated byadoes not grow in some directions and stabilizes to a positively homogeneous function. It is shown that the spectrum σ(H̃(a)) consists of σdisc(H̃(a)) and {0}, the latter being an isolated eigenvalue of infinite multiplicity, the former accumulating to +∞ only. The principal term of the asymptotics of σdisc(H̃(a)), and of σ(H(a)+V), wherebandVdo not grow in some directions, is computed