[Pw_forum] About wavefunction

[Jiqiang Li]

Dear Robert Hembree,
     I am sorry that I had something wrong in my expression before.
1)     Actually, I focus on the result of conjg(psi_1(r)) * psi_2(r), here both wavefunction belong to the same k point and 'conjg'  is complex conjugate operation. I agree with your conclusion that < psi_1(r) | psi_2(r) is a real number, which is also checked before by me.  However, conjg(psi_1(r)) * psi_2(r) is the array but not a number, and I want to clarify  whether the array is real array.
2)  We share the same result.

Best regards
Jiqiang Li
Fudan University, China



 
From: Robert Hembree
Date: 2015-04-17 14:07
To: 'PWSCF Forum'
Subject: Re: [Pw_forum] About wavefunction
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
      
 
 


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