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The Many-Electron Problem

Within the Born-Oppenheimer approximation[4], the time independent Schrödinger equation for a fully interacting many-electron system is


where tex2html_wrap_inline5833 is the N-electron wavefunction, tex2html_wrap_inline5837 are the electron positions, tex2html_wrap_inline5839 are the positions of the ions and tex2html_wrap_inline5841 are the ionic charges. This equation is impossible to solve exactly so approximate solutions must be sought. One of the main challenges of condensed matter physics is to try to find good, workable approximations that contain the essence of the physics involved in a particular problem and to obtain the most accurate solutions possible. For the rest of this thesis all equations will be written in atomic units, tex2html_wrap_inline5843 .

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