Schrdinger算子的Cauchy初值问题的唯一解

The Unique Solution of Cauchy Initial Value Problem about Schrdinger Operator

在具有Ricci曲率的有界维非紧致完备黎曼流形上考虑了关于加权Hodge-Laplacian的Schrdinger算子的初值Cauchy问题,证明了初值满足一定条件时该问题存在唯一解。

The Cauchy initial value problem about Schrodinger operator for weighted Hodge-Laplacian on a bounded n（n≥3） dimensional noncompact complete Riemann manifold（M,g）with Ricci curvature was considered in this paper. It was proved that there was a unique solution to this problem when the initial value satisfied a certain condition.