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Old Nov 1st 2018, 04:04 PM   #1
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equation

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Old Nov 1st 2018, 07:42 PM   #2
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Originally Posted by gab36 View Post
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Just so we don't all have to download the file the question is

If
$\displaystyle \psi (x) = \sum_{q}a_q e^{i q x}$

Then does the Schrodinger equation become:
$\displaystyle \sum_{q'} \left ( \dfrac{\hbar ^2 q'^2}{2m} e^{i q' x} + U e^{i (q' + g) x} + U e^{i (q' - g) x} \right ) a_{q'} = E \sum_{q} a_{q'} e^{i q' x}$

A few points. Why are you using q' instead of just q? Where did the g come from? And finally I'm presuming your potential energy function is U(x) but I can't see how you would have got that form. It should be
$\displaystyle U \psi = U ~ \sum_{q'} a_{q'} e^{i q' x}$

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Old Nov 2nd 2018, 04:00 AM   #3
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I think it's just a case of substituting the wave function and processing it with the operators. Have you given it a go?
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