SPECTRAL PROPERTIES OF SCHRODINGER-OPERATORS WITH IRREGULAR MAGNETIC POTENTIALS, FOR A SPIN-1 2 PARTICLE/

The two-dimensional Schrodinger operator (H) over tilde(a) for a spin 1/2 particle is considered. The magnetic field b generated by a does n ot grow in some directions and stabilizes to a positively homogeneous function. It is shown that the spectrum sigma((H) over tilde(a)) consi sts of sigma(disc)((H) over tilde(a)) and {0}, the latter bring an iso lated eigenvalue of infinite multiplicity, the former accumulating to +infinity only. The principal term of the asymptotics of sigma(disc)(( H) over tilde(a)), and of sigma(H(a) + V), where b and V do not grow i n some directions, is computed. (C) 1997 Academic Press.