Fredholmgleichungen fuer die 3-Teilchen-Resolvente von Schroedingeroperatoren MIT Langreichweitigen Potentialen (Fredholm Equations for the Three-Particle Resolver of Schroedinger Operators with Long Range Potentials)

摘要

The resolver of a three-particle Hamilton operator was investigated to deduce the scattering amplitudes for three-particle scattering processes. The case of long range potentials, to which the Coulomb potential belongs, was considered, with a limitation to negative global energy. Starting from the Faddeev equations for short range potentials, Fredholm equations on suitable Banach spaces were derived for the resolver. It is shown that these equations can be solved if no bound state exists for the corresponding energy. The equations conserve their Fredholm property after the transition to the real axis.