Position Operator

#Physics

$\displaystyle \hat{x}=x$

• Position operator in position space

$\displaystyle \hat{x}=\frac{x_{0}}{2}(\hat{a}{+}+\hat{a}{-})$

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

$\displaystyle \hat{x}=i\hbar \frac{ \partial }{ \partial p }$

• In momentum space