From "Modern Quantum Mechanics, revised edition" by J.J. Sakurai, page 196.(adsbygoogle = window.adsbygoogle || []).push({});

Equation (3.6.4),[tex]

1-i \left( \frac{\delta \phi}{\hbar} \right) L_z = 1 - i \left( \frac{\delta \phi}{\hbar} \right) (x p_y - y p_x )

[/tex]Making this act on an arbitrary position eigenket [itex]\mid x', y', z' \rangle[/itex],

Equation (3.6.5),[tex]

\begin{eqnarray}

\left[ 1-i \left( \frac{\delta \phi}{\hbar} \right) L_z \right] \mid x', y', z' \rangle & = & \left[ 1 - i \left( \frac{p_y}{\hbar} \right) ( \delta \phi x' ) + i \left( \frac{p_x}{\hbar} \right) ( \delta \phi y' ) \right] \mid x', y', z' \rangle \\

& = & \mid x' - y' \delta \phi, y' + x \delta \phi, z' \rangle

\end{eqnarray}

[/tex]

What I don't understand is, in equation (3.6.5), why did they operate by the position operators first, and not the momentum operators. Looking at equation (3.6.4), it looks like the ket [itex]\mid x', y', z' \rangle[/itex] should be operated on by the momentum operators first.

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# Sakurai page 196: Orbital angular momentum as rotation generator

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