Using cylindrical coordinates, the operators \phi and L_z are expressed as \phi and -i \hbar \frac{d}{d\phi} respectively, where these observables play a role similar to position and momentum for the particle in a box.
(\Delta \phi) (\Delta L_z) \geq \frac{\hbar}{2} where \Delta_{\psi} \phi = \sqrt{\langle {\phi}^2\rangle_\psi - \langle {\phi}\rangle_\psi ^2} and \Delta_{\psi} L_z = \sqrt{\langle {L_z}^2\rangle_\psi - \langle {L_z}\rangle_\psi ^2} \quad (9) .