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 >> > _______________________________________________ >> > 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
