相干态总结
Displacement operator
$$ D(\alpha) = e^{\alpha a^{\dagger} - \alpha^* a} $$
$$ \alpha a^{\dagger} - \alpha^* a = \mathrm{i} (\mathrm{Im}[\alpha] x - \mathrm{Re}[\alpha]p) $$
$$ e^{\mathrm{i} a p } \sim 1 - \mathrm{i} a p = 1 - a \frac{\partial}{\partial x} $$
$$ e^{\mathrm{i} a p } f(x)\sim f(x) - a \frac{\partial}{\partial x} f(x) = f(x - a) $$