[Pw_forum] symmetry of the electron-phonon coupling coefficients

[Alex Kutana]

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
>
>
>
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