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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Dear Jiqiang Li,<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><span style='mso-list:Ignore'>1)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>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. <o:p></o:p></span></p><p class=MsoNormal style='margin-left:.25in'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>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. <o:p></o:p></span></p><p class=MsoNormal style='margin-left:.25in'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>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. <o:p></o:p></span></p><p class=MsoNormal style='margin-left:.25in'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>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)<o:p></o:p></span></p><p class=MsoNormal style='margin-left:.25in'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>My suspicion is that you are doing something incorrectly. <o:p></o:p></span></p><p class=MsoNormal style='margin-left:.25in'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><span style='mso-list:Ignore'>2)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>In my experience no, not unless you force the Gamma point only calculation. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal style='margin-left:.25in'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>I apologize if the notation here doesn’t quite work out so well. Writing equations in text like this does not work well. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Robert Hembree<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'>Quantum Theory project. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> pw_forum-bounces@pwscf.org [mailto:pw_forum-bounces@pwscf.org] <b>On Behalf Of </b>Jiqiang Li<br><b>Sent:</b> Friday, April 17, 2015 12:59 AM<br><b>To:</b> pw_forum<br><b>Subject:</b> [Pw_forum] About wavefunction<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black'>Dear all,<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black'> 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.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black'> 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 <span style='background:white'>< psi_1 | psi_2 > was also a complex number.</span><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black;background:white'> Could you tell me the reason?</span><span style='font-size:10.5pt;font-family:"????",serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black;background:white'> 2. Is the wavefunction in real space form at Gamma point a series of real number? ( not only for the gamma point only calculation)</span><span style='font-size:10.5pt;font-family:"????",serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black;background:white'> Thanks for your consideration!</span><span style='font-size:10.5pt;font-family:"????",serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black;background:white'>Best regards!</span><span style='font-size:10.5pt;font-family:"????",serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black;background:white'>Jiqiang Li</span><span style='font-size:10.5pt;font-family:"????",serif;color:black'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black'>Fudan University, China<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black'><o:p> </o:p></span></p></div><div class=MsoNormal><span style='font-size:10.5pt;font-family:"????",serif;color:black'><hr size=1 width=210 style='width:157.5pt' noshade style='color:#B5C4DF' align=left></span></div></div></body></html>