  The Casimir energy is the first-order-in-\hbar correction to the energy of a
time-independent field configuration in a quantum field theory. We study the
Casimir energy in a toy model, where the classical field is replaced by a
separable potential. In this model the exact answer is trivial to compute,
making it a good place to examine subtleties of the problem. We construct two
traditional representations of the Casimir energy, one from the Greens
function, the other from the phase shifts, and apply them to this case. We show
that the two representations are correct and equivalent in this model. We study
the convergence of the Born approximation to the Casimir energy and relate our
findings to computational issues that arise in more realistic models.
