强磁场下的Schroedinger算子：奇点的奇性传播和更尖锐的渐近性
Schroedinger Operator with Strong Magnetic Field: Propagation of singularities and sharper asymptotics
摘要：
考虑非退化磁场下的二维薛定谔算子，讨论了其谱渐近性，给出了其馀项估计为$o(μ^{-1}h^{-1})$或更好的估计.我们还考虑了非简并磁场下的三维薛定谔算子，并讨论了其谱渐近性，其馀项估计为$o(μ^{-1}h^{-1})$或更好。我们还考虑了广义薛定谔-泡利算子在相同的框架下，虽然与$μh\ge 1$和推导谱渐近与剩余估计高达$O(h^{-1}|\log h|)$和主部$\asymp μh^{-2}$。
英文摘要：
We consider 2-dimensional Schrödinger operator with the non-degenerating magnetic field and we discuss spectral asymptotics with the remainder estimate $o(μ^{-1}h^{-1})$ or better. We also consider 3-dimensional Schrödinger operator with the non-degenerating magnetic field and we discuss spectral asymptotics with the remainder estimate $o(μ^{-1}h^{-1})$ or better. We also consider generalized Schrödinger-Pauli operator in the same framework albeit with $μh\ge 1$ and derive spectral asymptotics with the remainder estimate up to $O(h^{-1}|\log h|)$ and with the principal part $\asymp μh^{-2}$.
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