Spectral properties of Schrodinger operators with irregular magnetic potentials, for a spin 1/2 particle

[摘要] 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 not grow in some directions and stabilizes to a positively homogeneous function. It is shown that the spectrum sigma((H) over tilde(a)) consists of sigma(disc)((H) over tilde(a)) and {0}, the latter bring an isolated 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 in some directions, is computed. (C) 1997 Academic Press.

[发布日期] 1997-12-01