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 ${\displaystyle U(t)=e^{itD}}$, where ${\displaystyle D=\sum _{i,j}{a}_{ij}{\partial }_{x_j}{\partial }_{x_k}}$ in its general form, ${\displaystyle \sqrt{-1}=i}$ and ${\displaystyle x\in {\mathbb{ℝ}}^d}$.^[1][2]

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