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: [email protected] [mailto:[email protected]] 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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