Spectral properties of Schrödinger operators with irregular magnetic potentials, for a \(\text{spin }\frac{1}{2}\) particle (Q1378684)

Let \(H({\mathbf a})\) be two-dimensional Schrödinger operator for a spin \(1/2\) particle with magnetic field \({\mathbf a}\). If the magnetic field does not grow in some directions, it is proved that the spectrum of \(H({\mathbf a})\) is discrete except for 0, 0 is an isolated eigenvalue with infinite multiplicity. The principal term of the asymptotic of the discrete spectrum is computed also.