  In a finite volume, resonances and multi-hadron states are identified by
discrete energy levels. When comparing the results of lattice QCD calculations
to scattering experiments, it is important to have a way of associating the
energy spectrum of the finite-volume lattice with the asymptotic behaviour of
the S-matrix. A new technique for comparing energy eigenvalues with scattering
phase shifts is introduced, which involves the construction of an exactly
solvable matrix Hamiltonian model. The model framework is applied to the case
of $\Delta\rightarrow N\pi$ decay, but is easily generalized to include
multi-channel scattering. Extracting resonance parameters involves matching the
energy spectrum of the model to that of a lattice QCD calculation. The
resulting fit parameters are then used to generate phase shifts. Using a sample
set of pseudodata, it is found that the extraction of the resonance position is
stable with respect to volume for a variety of regularization schemes, and
compares favorably with the well-known Luescher method. The model-dependence of
the result is briefly investigated.
