Simple Soluble Model for the Decay of an Unstable State

A solution is presented for the decay of a discrete state to a continuum via a coupling of Lorentzian form, the continuum extending over all real energy values. Although the model is highly unrealistic, it is of interest because of the unusually simple analytic form of the results. The behavior of the decay solution is examined as a function of the coupling constant, and its relationship to the $S$ matrix is investigated.