Schrdinger算子的共振理论

Resonance Theory of Schrdinger Operators

1.引言 schrodinger算子的共振(resonances)问题是非相对论量子力学提出的最有趣、最具挑战性的数学问题之一。达既是由于共振问题在许多物理现象中占有重要的位置,也是由于这个问题在数学上的微妙性。自从本世纪初量子力学诞生以来,许多数学物理工作者致力于共振的研究,取得了不少进展。尤共是在近几年中,甘盆完善的近代偏微分方程理论,提供了越来越多的有力工具,使schrodinger算子共振理论的研究取得了引人注目的成就。达些工作不仅使许多抽象的数学理论在解释现实世界中得到了有意义的应用。

Modern theories of partial differential equations have beautiful applications to problems coming from mathematical physics. A convincing example is the study of Schrodinger operators. In this paper, we survey the results obtained by methods of microlocal analysis, on resonances of Schrodinger operators. In particular, the recent progresses made on the resonances in semiclassical limit and the resonances in Stark effect are presented. Some open problems related to resonances of Schro-dinger operators are also discussed.