If we want to solve
as
a matrix problem, we need to find a suitable linear vector space. Now
is an *N*-electron function that must be
antisymmetric with respect to interchange of electronic coordinates.
As we just saw in the previous section, any such *N*-electron function
can be expressed *exactly* as a linear combination of Slater
determinants, within the space spanned by the set of orbitals
.
If we denote our Slater determinant basis
functions as
,
then we can express the eigenvectors as

(167) |

for

If we solve this matrix equation,
,
in the space of all possible Slater determinants as
just described, then the procedure is called *full
configuration-interaction*, or full CI. A full CI constitues the *exact* solution to the time-independent Schrödinger equation within
the given space of the spin orbitals .
If we restrict the
*N*-electron basis set in some way, then we will solve Schrödinger's
equation *approximately*. The method is then called
``configuration interaction,'' where we have dropped the prefix
``full.'' For more information on configuration interaction, see the
lecture notes by the present author [7] or the review
article by Shavitt [8].