Hi, hope this is in the right thread, just a little stuck on a Quantum mechanics question.

$\displaystyle \Psi(x) = \sqrt{\frac{2}{a}} \sin{\frac{n \pi x}{a}}$ for $\displaystyle 0 < x < a$, zero otherwise.

I'm then asked to calculate the dispersion $\displaystyle \Delta x$ and the dispersion $\displaystyle \Delta p$. For n = 1, show $\displaystyle \Delta x \Delta p > \frac{\hbar}{2}$

I can easily calculate $\displaystyle \Delta x$, but I'm not really sure about $\displaystyle \Delta p$, which I'm taking as the dispersion of the momentum?

I've tried calculating the expectation of the momentum as:

$\displaystyle \int^a_0 -i \hbar \frac{d}{dx} (\sqrt{\frac{2}{a}} \sin{\frac{n \pi x}{a}})^2$ and following it through this way, but then this gave me the dispersion of the momentum as zero, which doesn't fit in with the question.

Any help on this would be greatly appreciated.

Thanks in advance

Craig