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Thread: Quantum theory wave functions

  1. April 16th 2010, 07:44 AM #1
    charlie112
    charlie112 is offline
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    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!
    Last edited by charlie112; April 16th 2010 at 09:45 AM.
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