1. The problem statement, all variables and given/known data
Given that $\hat{p} = -i\hbar (\frac{\partial}{\partial r} + \frac{1}{r})$, show that $\hat{p}^2 = -\frac{\hbar^2}{r^2} \frac{\partial}{\partial r}(r^2 \frac{\partial}{\partial r})$

2. Relevant equations

Above

3. The attempt at a solution
I tried $\hat{p}\hat{p} = -\hbar^2((\frac{\partial}{\partial r})^2 + \frac{1}{r} \frac{\partial}{\partial r} + \frac{\partial}{\partial r}\frac{1}{r} +\frac{1}{r^2})$.

This gave me $-\hbar^2((\frac{\partial}{\partial r})^2 + \frac{1}{r} \frac{\partial}{\partial r} )$ instead of the 2 / r factor I needed.

http://ift.tt/1hIrcZU