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One-Electron Methods

One of the most common ways of dealing with the many-fermion problem is to assume that each electron can be considered separately. Each electron is treated as moving in a mean field potential, tex2html_wrap_inline5845 . This potential models the effects of all the other particles in the system, as well as any external potential acting on the system.

The one-electron equations are of the form


where tex2html_wrap_inline5847 is a one-electron wavefunction and tex2html_wrap_inline5849 are Lagrange multipliers which arise from the fact that the one-electron wavefunctions are normalised. Choosing an appropriate tex2html_wrap_inline5845 for the single electron is still a very complicated problem. tex2html_wrap_inline5845 depends upon the interactions between the electrons and therefore on the one-electron wavefunctions. Since initially neither of these quantities, tex2html_wrap_inline5845 or tex2html_wrap_inline5847 , is known, it is necessary to solve Eq.(gif) in a self-consistent manner.

Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996