[QE-users] A DFPT equation

[Andrew Xu]

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
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