Lecture: ab initio Methods Appendix:Schrodinger Picture Eigenproblem

Using the principle of least action from classical mechanics, the linear operator H in

equation367

corresponds to Hamilton's function for a mechanical system. If the system is not in a time varying field, then H does not contain the time explicitly. A Hamilton's function, which is conserved, is called the energy. The corresponding quantum states are called stationary states

equation371

Electron K.E. term of Hamiltonian

eqnarray373

where N = number of electrons and both operators act on tex2html_wrap_inline565.
tex2html_wrap_inline565 is a scalar valued function of 3N variables.

eqnarray386

tex2html_wrap_inline761 = Probability Density Function (PDF) of electrons at point x,y,z.

eqnarray391

Pr(an electron is in region V) = tex2html_wrap_inline763
tex2html_wrap_inline565 is a function of some variables (electrons) and some parameters

eqnarray395

tex2html_wrap_inline565 is a function of 3N + 3A parameters
tex2html_wrap_inline565 (really tex2html_wrap_inline601 ) is a complex (scalar) valued function of positions of electrons.
(recall tex2html_wrap_inline773 )

eqnarray402

eqnarray406



Author: Ken Flurchick