[Pw_forum] About wavefunction

[Robert Hembree]

Dear Jiqiang Li,

1)      If you compute <psi_i|psi_j> at the same point then the result is
delta_ij. If the bands are different at the same kpoint then you will get
zero for this value. 

If you are outputting the wavefunction at <psi_1|psi_2> and getting a
complex number other than 0+0i or some other sufficiently small number I
suspect you are doing it incorrectly. For example when I compute these
values I get a value on the order of 10^-17. 

Perhaps if you modified your wavefunction. It should instead read psi_j(k,r)
= sum_G C_j,G(k) exp(-(G+k)*r)) as a plane wave description would generally
require. 

If you work it out by hand then the overlap will be <psi_i|psi_j> = sum_G
C*_i,G(k) C_j,G(k)

My suspicion is that you are doing something incorrectly.    

 

2)      In my experience no, not unless you force the Gamma point only
calculation. 

 

I apologize if the notation here doesn't quite work out so well. Writing
equations in text like this does not work well. 

Robert Hembree

Quantum Theory project.  

 

From: pw_forum-bounces at pwscf.org [mailto:pw_forum-bounces at pwscf.org] On
Behalf Of Jiqiang Li
Sent: Friday, April 17, 2015 12:59 AM
To: pw_forum
Subject: [Pw_forum] About wavefunction

 

Dear all,

  1.    In Quantum Espresso, do wavefunction in real space form at the same
k point  share the same phase? i.e.,  psi_1(r) = A(r)exp(ikr) and
psi_2(r)=B(r)exp(ikr), psi_1 and psi_2 belong to different bands at same k
point.

        If so, we should find the vaule < psi_1 | psi_2 > =
A(r)exp(-ikr)*B(r)exp(ikr)=A(r)B(r), which is a series of real number.
However, I output the wavefunctions and found < psi_1 | psi_2 > was also a
complex number.

        Could you tell me the reason?

  2.   Is the wavefunction  in real space form at Gamma point a series of
real number? ( not only for the gamma point only calculation)

    Thanks for your consideration!

 

Best regards!

 

Jiqiang Li

Fudan University, China

      

 

 

  _____  

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20150417/79517390/attachment.html>