[Pw_forum] Orthogonality of wavefunctions

[Paolo Giannozzi]

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