Quantal rules for non-hermitian bound state formalisms based on N-body scattering theory

One of the interesting recent developments in the areas of few-body physics and many-body scattering theory has been the application of some of the scattering theory equations to the structure of simple (few-body) atoms and molecules. The results obtained to date fall into two classes: (a) that consisting of relatively accurate values of observables obtained using relatively simple approximate wave functions, and (b) that containing all other results, consisting mainly of complex energy eigenvalues, spurious (real energy) solutions, and non-monotonically converging sets of energies. Since calculations are based on approximations to a non-hermitian operator equation, questions naturally arise concerning the meaning of these two classes, the nature of the eigenvalue spectrum, and the rules for interpreting results, e.g., how to compute probability and charge densities. (orig./WL)