论文标题
在动态schrödinger方程中恢复时间依赖性的Hermitian连接和潜力
Recovery of a time-dependent Hermitian connection and potential appearing in the dynamic Schrödinger equation
论文作者
论文摘要
我们考虑在一个带有边界的Riemannian歧管上的微不足道的载体束上，这是从Dirichlet到Neumann Map的知识中恢复动态，矢量值schrödinger方程的独特时间和空间依赖性系数。我们表明，在schrödinger方程中，d-to-n map唯一确定了连接形式和出现的电势，假设歧管是a）二维和简单的，或者b）具有严格凸边界的较高维度的较高维度，并且承认平稳的，严格地凸出功能。
We consider, on a trivial vector bundle over a Riemannian manifold with boundary, the inverse problem of uniquely recovering time- and space-dependent coefficients of the dynamic, vector-valued Schrödinger equation from the knowledge of the Dirichlet-to-Neumann map. We show that the D-to-N map uniquely determines both the connection form and the potential appearing in the Schrödinger equation, under the assumption that the manifold is either a) two-dimensional and simple, or b) of higher dimension with strictly convex boundary and admits a smooth, strictly convex function.
