论文标题
在间隔上对半经典schr的均匀观察
Uniform observation of semiclassical Schr{ö}dinger eigenfunctions on an interval
论文作者
论文摘要
我们考虑半经典schr {Ö} dinger操作员的本征函数，具有单孔型电势和差点边界条件。我们在半经典和高能量限制中均匀的特征函数的L^2密度给出上/下边界。这些界限是最佳的，并且在适用于可控性问题的同伴论文中以必不可少的方式使用。证据依赖于经典禁止区域中的Agmon估计和Gronwall类型参数，以及对经典区域中边界价值问题的半经典措施的描述。假定有限的规律性。
We consider eigenfunctions of a semiclassical Schr{ö}dinger operator on an interval, with a single-well type potential and Dirichlet boundary conditions. We give upper/lower bounds on the L^2 density of the eigenfunctions that are uniform in both semiclassical and high energy limits. These bounds are optimal and are used in an essential way in a companion paper in application to a controllability problem. The proofs rely on Agmon estimates and a Gronwall type argument in the classically forbidden region, and on the description of semiclassical measures for boundary value problems in the classically allowed region. Limited regularity for the potential is assumed.
