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Kohn-Sham equations from variational principle

The Kohn-Sham equations arise from variation in terms of orbitals, not the total density. See for example Fundamentals of DFT by Eschrig, 2nd ed., Sec. 4.2.
Mage's user avatar
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Is there an error in Susskinds' derivation of Euler-Lagrange equations?

In order to add more context to anyone else that stumbles upon this, in the book directly above the screenshot posted, the author defines the action as follows: $$A = \sum_{n} L\left(\frac{{x_{n+1}} - ...
kenzzo13's user avatar
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Auto-parallel Transport or Principle of Extremum Action?

Both equations are equivalent. Recall that torsion is the antisymmetric part of the connection coefficients, but in the auto-parallel curve equation only the symmetric part contributes. Namely, $$\...
Níckolas Alves's user avatar
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Calculus of variations -- how does it make sense to vary the position and the velocity independently?

I want to start with asserting that nowhere in the evaluation there is a stage where the two factors $y$ and $\tfrac{dy}{dx}$ are treated as independent. The purpose of this answer is to address the ...
Cleonis's user avatar
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Boundary conditions in $\delta I=0$ to derive Einstein's equations -- why the derivatives of $g_{\mu\nu}$ are held constant?

The Einstein–Hilbert action is incomplete. It involves a boundary term with contains second derivatives of the metric, but which does not affect the resulting Einstein equations (if you derive them ...
Níckolas Alves's user avatar

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