# Math Help - Quantum theory wave functions

1. ## Quantum theory wave functions

How would I go about answering this question?

A particle of mass m moves freely in the interval [0,a] on the x-axis (so that the potential V = 0 within the interval). Initially the wave function is

$\frac{1}{\sqrt{a}}\sin{\left (\frac{\pi x}{a} \right )}\left (1+2\cos{\left (\frac{\pi x}{a} \right )} \right )$.

Show that at a later time t the wave function is

$\frac{1}{\sqrt{a}}e^{-i \pi^2 h t/2ma^2 }\sin{\left (\frac{\pi x}{a} \right )}\left (1+2e^{-3i \pi^2 h t/2ma^2} \cos{\left (\frac{\pi x}{a} \right )} \right )$.

Note that the h's in the formula above are supposed to be h-bars, but I don't know how to write them in LaTeX.

Thanks to anyone for any help you can give me!