Dear Stefano, Thank you for your explanation. I incorrectly assumed that translation should leave the matrix element invariant, which is false, since wavefunctions actually stay fixed. Thanks again for your help.
Alex On Thu, May 10, 2012 at 4:56 PM, Stefano de Gironcoli <degironc at sissa.it>wrote: > ** > dear Alex > > I don't think that the two matrix element should be equal and opposite. > suppose you apply both displacement together which means you displace > the molecule as a whole. > > the eigenvalue will not change, hence < i | dV | i > = 0 > but the new eigen-wavefunctions | i' > will be the translated of the > original ones, hence different from them. > to first order |i'> = |i> + sum |j> <j|dv|i>/delta e_IJ > since |i'> =/= |i> no reason to believe that < j | d V | i > = 0. > > stefano > > > -------------- next part -------------- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20120510/08cb0669/attachment.htm
