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 [math]\displaystyle{ U(t) =e^{i tD } }[/math], where [math]\displaystyle{ D=\sum_{i,j}a_{ij}\partial_{x_j}\partial_{x_k} }[/math] in its general form, [math]\displaystyle{ \sqrt{-1}=i }[/math] and [math]\displaystyle{ x \in \mathbb{R}^d }[/math].[1][2]

## Example

## References

1. ↑ Sulem C. Sulem P. The Nonlinear Schrodinger Equation, Self-focusing and wave collapse. p. 43, 51
2. ↑ Sakurai, J. J. . "Modern Quantum Mechanics". MIT, reading p. 68.

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