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## Homework Statement

Derive the infinitesimal rotation operator around the z-axis.

## Homework Equations

My book gives this equation (which I follow) with epsilon the infinitesimal rotation angle:

$$ \hat{R}(\epsilon) \psi(r,\theta, \phi) = \psi(r,\theta, \phi - \epsilon) $$

but I just don't get the next line in the book:

$$ \approx \psi(r,\theta, \phi) - \epsilon \frac{\partial \psi(r,\theta, \phi)}{\partial \phi} + \frac{\epsilon^2}{2} \frac{\partial^2 \psi(r,\theta, \phi)}{\partial \phi^2} ...$$

## The Attempt at a Solution

I was expecting something like

$$ =(1-\epsilon) \psi(r,\theta, \phi) $$

I can see the books Eq is a series, but just can't see how they get to it, with partial diffs as well?