Completeness of stationary scattering states. II

Synopsis The question is to what extent the usual concepts apply to the general form of the S matrix envisaged in Part I, viz., an S that is not holomorphic in the upper half plane, but for which the stationary scattering states are still a complete set. The answer is that it is again possible to find the explicit expansion of an arbitrary function with respect to this set, so that the evolution of an arbitrary initial state can be calculated. Emission can be described by choosing a superposition of stationary states in such a way that the wave function vanishes initially. Resonance levels and excited states, however, can only be uniquely defined if an analytic continuation of S is possible.