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
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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].