# [QE-users] How is the wavefunction supposed to be normalized?

Paolo Giannozzi p.giannozzi at gmail.com
Wed Dec 12 13:18:09 CET 2018

```On Tue, Dec 11, 2018 at 7:09 PM John McFarland <jm18ec at my.fsu.edu> wrote:

>
> I forgot to ask if different bands are orthogonal for the contraction over
> the S matrix.
>

yes, they are

Paolo

>
> John
> ------------------------------
> *From:* users <users-bounces at lists.quantum-espresso.org> on behalf of
> Stefano de Gironcoli <degironc at sissa.it>
> *Sent:* Tuesday, December 11, 2018 10:26:15 AM
> *To:* users at lists.quantum-espresso.org
> *Subject:* Re: [QE-users] How is the wavefunction supposed to be
> normalized?
>
>
> yes, except the S matrix is never stored anywhere but is applied to the
> wfc by the s_1psi routine,
>
> so more something like
>
>
>  sum = 0.d0
>
>  call s_1psi( npwx, npw, evc(1,b), spsi )
>
>  DO  i = 1,npw
>
>      sum = sum + conjg(evc(i,b)) * spsi(i)
>  END DO
>
>
>
>
> stefano
>
>
> On 11/12/18 15:36, John McFarland wrote:
>
> Dear all,
>
>
> As I understand it, the wavefunction for each k-point is given by
> ecv(:,:), with the first index representing a single particle basis and the
> second index representing each band.  I'm guessing that when a normalized
> wavefunction is contracted over the S matrix, the result should equal one
> for each band.  What I think this would look like in code is:
>
>
>  sum = 0
>
>  DO  i = 1,npwx
>
>     DO j = 1,npwx
>
>        sum = sum + evc(i,b) * S(i,j) * evc(j,b)
>
>     END DO
>
>  END DO
>
>
> and sum should equal 1 for any band b.  Is my understanding correct?
>
>
> Best regards,
>
> John McFarland
>
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--
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
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