A method for quantizing scalar theories with unstable ground states is presented. The collapse of the ground-state vacuum bubble is modeled in an $S$-matrix formulation by using different coherent states for the incoming and outgoing ground states. Time-dependent coherent-state functions corresponding to a single vacuum bubble in both one and three spatial dimensions are found and seen to disperse. The amplitude for producing an arbitrary number of particles through collapse is reduced and given a perturbative representation. The $\ensuremath{\lambda}{\ensuremath{\psi}}^{4}$ model is analyzed in three dimensions and the average number of particles produced is calculated to lowest order. This is related to vacuum bubbles in the early Universe and subsequent particle production through the standard model.