论文标题
1D单数schrödinger操作员的特征值间距
Eigenvalue spacing for 1D singular Schrödinger operators
论文作者
论文摘要
本文的目的是为一维半经典的schrödinger操作员的特征值间距提供均匀的估计值，在半线上具有奇异的电位。我们介绍了与Schrödinger经营者家族有关的半经典措施的新开发，该措施提供了一种在该类别的运营商中建立统一的非浓度估计的方法。这种大大简化了分析，通常需要在转弯点附近，附近的奇异点和几种粘合类型的结果来连接域中的各个区域。
The aim of this paper is to provide uniform estimates for the eigenvalue spacings of one-dimensional semiclassical Schrödinger operators with singular potentials on the half-line. We introduce a new development of semiclassical measures related to families of Schrödinger operators that provides a means of establishing uniform non-concentration estimates within that class of operators. This dramatically simplifies analysis that would typically require detailed WKB expansions near the turning point, near the singular point and several gluing type results to connect various regions in the domain.
