If we want to solve
as
a matrix problem, we need to find a suitable linear vector space. Now
is an -electron function that must be
antisymmetric with respect to interchange of electronic coordinates.
As we just saw in the previous section, any such -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

(195) |

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
-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 one of
the available review articles [8,9].