Physics:Linear Schrödinger Operator

A linear Schrödinger operator is an exponential operator used in the theory of Schrödinger equation in expressing solution of Schrödinger equation in an integral form. It is essentially defined by $U(t)=e^{itD}$, where $D=\sum _{i,j}{a}_{ij}{\partial }_{x_j}{\partial }_{x_k}$ in its general form, $\sqrt{-1}=i$ and $x\in {\mathbb{ℝ}}^d$.