Position Operator

$\hat{x}=x$

• Position operator in position space

$\hat{x}=\frac{x_0}{2}({\hat{a}}_{+}+{\hat{a}}_{-})$

• $x_0$ is the characteristic length
• ${\hat{a}}_{+}$ is the raising operator
• ${\hat{a}}_{-}$ is the lowering operator

$\hat{x}=i\hslash \frac{\partial }{\partial p}$

• In momentum space