Insert Eq.61 into Eq.59. You will get Eq.62, plus a higher-order term. Paolo
On Fri, Feb 19, 2021 at 12:52 AM Andrew Xu <andrewacco...@gmail.com> wrote: > Hi users, > > I had a question about one of the DFPT equations in Baroni et al. "Phonons > and related crystal properties from DFPT." I was unsure about posting this > question here because most of the questions here are about using QE, but I > choose to do so since DFPT is implemented in QE, the authors are on this > mailing list, and in case someone else had the same question. > > I'm curious how we arrive at the LHS of equation 62 (H - epsilon) |Delta > psi>. It appears that we started from equation 59 and rearranged the RHS to > arrive at equation 62, so I would expect the LHS to remain the same. Yet > the LHS of both equations differ ((H - epsilon) |Delta psi> and H |Delta > psi> - sum(Lambda |\Delta psi>). > > My initial thought was do to the same thing done in equation 52 in moving > to the canonical KS equations, but it is not obvious to me how that might > change H |Delta psi> - sum(Lambda |\Delta psi>) to (H - epsilon) |Delta > psi> because they are acting on the perturbed wavefunctions, whereas the > unitary was defined based on linear combinations on the KS wavefunctions. > > Best regards, > Andrew > _______________________________________________ > Quantum ESPRESSO is supported by MaX (www.max-centre.eu) > users mailing list users@lists.quantum-espresso.org > https://lists.quantum-espresso.org/mailman/listinfo/users -- Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche, Univ. Udine, via delle Scienze 206, 33100 Udine, Italy Phone +39-0432-558216, fax +39-0432-558222
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