Ground state energy for a model gas in one dimension

Ground state energies of many-body systems in one dimension in the thermodynamic limit are calculated. We use relations between the ground state energy and the scattering phase, which are exact for a delta-function potential, and are fulfilled approximately for other interactions. This will be applied to a model of quantum field theory, for which theS-matrix can be calculated exactly by means of a property which is called factorization.