The Casimir energy in a separable potential

The Casimir energy is the first-order-in-h correction to the energy of a ti me-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 s eparable potential. III this model the exact answer is trivial to compute, making it a good place to examine subtleties of the problem. We construct t wo traditional representations of the Casimir energy, one from the Green's function and the other From the phase shifts, and apply them to this case. We show that the two representations are correct and equivalent in this mod el. We study the convergence of the Born approximation to the Casimir energ y and relate our findings to computational issues that arise in more realis tic models. (C) 2000 Academic Press.