Dear Stefano,<br><br>Thank you for your explanation.<br>I incorrectly assumed that translation should leave the matrix element invariant, which is false, since wavefunctions actually stay fixed.<br>Thanks again for your help.<br>
<br>Alex<br><br><div class="gmail_quote">On Thu, May 10, 2012 at 4:56 PM, Stefano de Gironcoli <span dir="ltr"><<a href="mailto:degironc@sissa.it" target="_blank">degironc@sissa.it</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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dear Alex<br>
<br>
I don't think that the two matrix element should be equal and
opposite.<br>
suppose you apply both displacement together which means you
displace the molecule as a whole.<br>
<br>
the eigenvalue will not change, hence < i | dV | i > = 0<br>
but the new eigen-wavefunctions | i' > will be the translated
of the original ones, hence different from them.<br>
to first order |i'> = |i> + sum |j> <j|dv|i>/delta
e_IJ<br>
since |i'> =/= |i> no reason to believe that < j | d V |
i > = 0.<br>
<br>
stefano<div><div class="h5"><br>
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