Momentum Operator

$\hat{p}=-i\hslash \nabla$

• Momentum operator in position space

$\hat{p}=\frac{i{p}_0}{2}({\hat{a}}_{+}-{\hat{a}}_{-})$

• $p_0$ is the characteristic momentum
• ${\hat{a}}_{+}$ is the raising operator
• ${\hat{a}}_{-}$ is the lowering operator

$\hat{p}=p$

• In momentum space

$p_x=-i\hslash {\partial }_x$

• Momentum operator in one dimension