[Pw_forum] Orthogonality of wavefunctions

[Zbigniew Koziol]

As I understand, orthogonality in this case follows from k's different 
numbers. Here does not matter how they overlap. Different quantum 
numbers, not space distribution.

zb.

On 02/11/13 16:58, Paolo Giannozzi wrote:
> 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
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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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