Spectral Properties of Schr¨odinger Operators with Irregular Magnetic Potentials, for a Spin 1 Particle

The two-dimensional Schr¨odinger operator H˜ a. for a spin 1 particle is consid- 2 ered. The magnetic field b generated by a does not grow in some directions and stabilizes to a positively homogeneous function. It is shown that the spectrum s H˜ a.. consists of sdi sc H˜ a.. and 04, the latter being an isolated eigenvalue of infinite multiplicity, the former accumulating to q` only. The principal term of the asymptotics of sdi sc H˜ a.., and of s H a.qV., where b and V do not grow in some directions, is computed