Using the principle of least action from classical mechanics, the linear operator H in
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
Electron K.E. term of Hamiltonian
where N = number of electrons and both operators act on
.
is a scalar valued function of 3N variables.
= Probability Density Function (PDF) of electrons
at point x,y,z.
Pr(an electron is in region V) =
is a function of some variables (electrons) and some parameters
is a function of 3N + 3A parameters
(really
)
is a complex (scalar) valued function of positions of electrons.
(recall
)