  The spectral shift function \xi_{L}(E) for a Schr\"odinger operator
restricted to a finite cube of length L in multi-dimensional Euclidean space,
with Dirichlet boundary conditions, counts the number of eigenvalues less than
or equal to E \in \RR created by a perturbation potential V. We study the
behavior of this function \xi_{L}(E) as L to infinity for the case of a
compactly-supported and bounded potential V. After reviewing results of Kirsch
[Proc. Amer. Math. Soc. 101, 509-512 (1987)], and our recent pointwise
convergence result for the Ces\`aro mean [Proc. Amer. Math. Soc. 138, 2141-2150
(2010)], we present a new result on the convergence of the energy-averaged
spectral shift function that is uniform with respect to the location of the
potential V within the finite box.
