If we want to solve
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
, then we can express the eigenvectors as
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  or one of the available review articles [8,9].