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S18a. What is the meaning of 'self-consistent'?
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A self-consistent solution (or method, or theory) refers to the fact
that one has two sets of equations relating two sets of unknown
quantities, and wants to solve the equations jointly for the unknowns.
If aspect A of a theory says y=x^2 and aspect B of the theory
(or of another theory) says x=y-2 then self-consistency means that
both equations are assumed to be valid, giving
x^2 = y = x+2,
which leads to the two solutions
x=2, y=4 and x=-1, y=1.
That's all. Of course, the self-consistent Hartree-Fock method,
say, has more variables and is harder to solve, but the principle
is the same.