- #1

Kashmir

- 468

- 74

##\begin{aligned}\langle r\rangle &=\langle n \ell m|r| n \ell m\rangle=\langle 100|r| 100\rangle \\ &=\int r\left|\psi_{n \ell m}(r, \theta, \phi)\right|^{2} d V \end{aligned}##

Since Hilbert space operators act on kets, What operator is ##r## in the expression :

##\begin{aligned}\langle r\rangle &=\langle n \ell m|r| n \ell m\rangle=\langle 100|r| 100\rangle \end{aligned}##

Is it a component of the position operator ##\mathbf x## that is related to the radial distance ?

Does it act on kets as:

##\hat{r}|r \theta \phi\rangle=r|r \theta \phi\rangle##