Normalizable Wave Functions for Bound States and Resonances inS-Matrix Theory

Normalizable wave functions are constructed for bound states and resonances from the $S$-matrix quantities. The bound-state wave function is of the Schrödinger type. The Schrödinger equation does not give normalizable wave functions for resonances. Thus the resonance wave function is of the non-Schrödinger type. An $S$-matrix model is constructed to generate the desired resonance wave function. The manner in which this model departs from the conventional Schrödinger picture is discussed in detail. This $S$-matrix model is then applied to the $P$-wave two-pion system with a satisfactory numerical result for the $\rho$-meson radius.