Schroedinger Operator with Strong Magnetic Field: Propagation of singularities and sharper asymptotics

We consider 2-dimensional Schr"odinger operator with the non-degenerating magnetic field and we discuss spectral asymptotics with the remainder estimate $o({\mu }^{-1}{h}^{-1})$ or better. We also consider 3-dimensional Schr"odinger operator with the non-degenerating magnetic field and we discuss spectral asymptotics with the remainder estimate $o({\mu }^{-1}{h}^{-1})$ or better. We also consider generalized Schr"odinger-Pauli operator in the same framework albeit with $\mu h\ge 1$ and derive spectral asymptotics with the remainder estimate up to $O(h^{-1}\mathrm{\mid }\log h\mathrm{\mid })$ and with the principal part $\asymp \mu h^{-2}$.