Plane Waves for the 3 Body Schrödinger Operator

Research Report MRR96-061

Plane Waves for the 3 Body Schrödinger Operator

Andrew Hassell

Abstract: Plane waves of energy $\lambda^2 > 0$, incoming in the free region, are constructed for generalized 3 body Schr\"odinger operators on $\RR^N$, under the assumption that the `two-body' potential functions are rapidly decreasing. The construction yields the form of the complete asymptotic expansion of the plane waves at infinity away from the cluster sets, that is, the subset of the boundary of radially compactified $\RR^N$ where the total potential does not decay to zero, and gives an explicit construction of the singularities of the 3-cluster to 3-cluster part of the scattering matrix.

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