Schr dinger算子的逆谱问题
Inverse Spectral Problem for Schrödinger Operators
摘要：
本文改进了Guillemin和Uribe在\cite{GU}中证明的一些逆谱结果.他们证明了在对势$V(x)$的某些对称性假设下，$V(x)$在非退化全局极小值附近的泰勒展开可以从$\mathbb R^n$中相关薛定谔算子的低本征值的知识中恢复。我们证明了一些类似的逆谱结果使用较少的对称性假设。我们还表明，在1维，没有对称性的假设是需要恢复的泰勒系数的$V(x)$。我们建立我们的结果，找到一些明确的公式波不变量在井底。
英文摘要：
In this article we improve some of the inverse spectral results proved by Guillemin and Uribe in \cite{GU}. They proved that under some symmetry assumptions on the potential $V(x)$, the Taylor expansion of $V(x)$ near a non-degenerate global minimum can be recovered from the knowledge of the low-lying eigenvalues of the associated Schrödinger operator in $\mathbb R^n$. We prove some similar inverse spectral results using fewer symmetry assumptions. We also show that in dimension 1, no symmetry assumption is needed to recover the Taylor coefficients of $V(x)$. We establish our results by finding some explicit formulas for wave invariants at the bottom of the well.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
