# Self consistent solution

1. Jun 21, 2009

### saray1360

what does self consistent solution mean in for example Kohn-sham equations?

2. Jun 21, 2009

### Astronuc

Staff Emeritus
The equations of a linear system are consistent if they possess a common solution, and consistency implies at least one solution.

See - http://en.wikipedia.org/wiki/System_of_linear_equations#Consistency

Self-consistency is the condition that $$F[n(\vec{x})]\,-\,n(\vec{x}) = 0$$.

See - section 4.4 of http://people.ccmr.cornell.edu/~muchomas/P480/Notes/dft/dft.pdf
from http://people.ccmr.cornell.edu/~muchomas/P480/

See also the original Kohn-Sham paper - "Self-Consistent Equations Including Exchange and Correlation Effects," by W. Kohn and L. J. Sham, Physical Review 140, A1133-A1138 (1965).
http://www.cem.msu.edu/~cem883/topics_pdf/Kohn_Sham.pdf

and

"Inhomogeneous Electron Gas," by P. Hohenberg and W. Kohn, Physical Review 136, B864-B871 (1964).
http://prola.aps.org/pdf/PR/v136/i3B/pB864_1 [Broken]