[Pw_forum] Orthogonality of wavefunctions

[Paolo Giannozzi]

More exactly: no, unless you integrate over the entire
space (not over a single cell).

P.

On Thu, 2013-10-31 at 10:11 -0400, Bo Qiu wrote:
> 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
>         > _______________________________________________
>         > Pw_forum mailing list
>         > Pw_forum at pwscf.org
>         > http://pwscf.org/mailman/listinfo/pw_forum
>         
>         --
>          Paolo Giannozzi, Dept. Chemistry&Physics&Environment,
>          Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
>          Phone +39-0432-558216, fax +39-0432-558222
>         
>         _______________________________________________
>         Pw_forum mailing list
>         Pw_forum at pwscf.org
>         http://pwscf.org/mailman/listinfo/pw_forum
> _______________________________________________
> Pw_forum mailing list
> Pw_forum at pwscf.org
> http://pwscf.org/mailman/listinfo/pw_forum

-- 
Paolo Giannozzi, Dept. Chemistry&Physics&Environment, 
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222