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 $O(h^{ -1}|\log h|)$ and with the principal part $\asymp \mu h^{ -2}$.
Categories: math.SP math.AP