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

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

2010-05-04

arxiv.org/abs/1005.0486v1

Mathematics

Spectral Theory

19 pp, 10 figs

Scientific paper

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 $\asymp \mu h^{-2}$.

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