[Pw_forum] Orthogonality of wavefunctions

[Bo Qiu]

Dear Paolo,

Thanks for pointig that out! So if I use the real space representation of
the periodic wavefunction (from cft_wave(evc)) with correct igk and later
multiply them by exp（ikr）and integrate in a real space volume, they should
give me the orthogonality for different k k'?

Thanks a lot,
Bo
On Oct 31, 2013 6:07 AM, "Paolo Giannozzi" <paolo.giannozzi at uniud.it> wrote:

> Bloch states at different k are orthogonal because they have different
> k, not because their periodic parts are orthogonal, so your test is not
> a valid one. Note that you have to take into account the different
> ordering of plane waves (array igk) at k and k' when computing
> <k| something |k'>
>
> P.
>
> On Thu, 2013-10-31 at 02:13 -0400, Bo Qiu wrote:
> > Dear developers and users,
> >
> >
> > I'm trying to compute some matrix elements between states k and k'. To
> > confirm my calculation, I first try to compute the overlap between
> > wavefunction k and k' as  < k| k'> in quantum espresso by taking zdoc
> > of state k and k' (modified the elphonon.f90 code). I do find for the
> > same k point, the overlap between different bands are 0. However, the
> > overlap between two states at different points k and k' are almost
> > always non-zero, indicating they're not orthogonal. I thought in
> > theory they should all be orthonormal because they belong to the same
> > Hamiltonian of the entire system. So is it because of numerical
> > reasons that they're actually not orthogonal in quantum espresso?
> >
> >
> > Thanks a lot for you help!
> >
> >
> > Bo
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>
> --
>  Paolo Giannozzi, Dept. Chemistry&Physics&Environment,
>  Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
>  Phone +39-0432-558216, fax +39-0432-558222
>
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