薛定谔算子的半经典谱不变量
Semiclassical Spectral Invariants for Schrödinger Operators
摘要：
本文研究了$R^n$上薛定谔算子的半经典谱测度。特别地，我们计算了这些测度的渐近展开的前几个系数，作为应用，给出了Colin de Verdiere关于从半经典谱数据恢复一维势阱的结果的另一种证明。我们还研究了半经典谱措施的Birkhoff规范形式的关系，并描述了一个推广的渐近展开上述薛定谔算子在磁场的存在下。
英文摘要：
In this article we study the semiclassical spectral measures associated with Schrödinger operators on $R^n$. In particular we compute the first few coefficients of the asymptotic expansions of these measures and, as an application, give an alternative proof of Colin de Verdiere's result on recovering one dimensional potential wells from semiclassical spectral data. We also study the relation of semiclassical spectra measures to Birkhoff normal forms and describe a generalization of the asymptotic expansion above to the Schrödinger operator in the presence of a magnetic field.
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