Momentum Operator

#Physics

$\displaystyle \hat{p}=-i\hbar \nabla$

• Momentum operator in position space

$\displaystyle \hat{p}=\frac{ip_{0}}{2}(\hat{a}{+}-\hat{a}{-})$

• $\displaystyle p_{0}$ is the characteristic momentum
• $\displaystyle \hat{a}_{+}$ is the raising operator
• $\displaystyle \hat{a}_{-}$ is the lowering operator

$\displaystyle \hat{p}=p$

• In momentum space

$\displaystyle p_{x}=-i\hbar \partial _x$

• Momentum operator in one dimension