## Distorted plane waves for the 3 body Schrödinger operator.(English)Zbl 0953.35122

Distorted plane waves, incoming in the free region, are constructed for generalized three-body Schrödinger operators on $$\mathbb{R}^N$$, 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 collision planes, and gives an explicit construction and geometric characterization of the singularities of the free channel scattering matrix.

### MSC:

 35Q40 PDEs in connection with quantum mechanics 81U10 $$n$$-body potential quantum scattering theory 35P25 Scattering theory for PDEs

### Keywords:

Schrödinger equation; three-body scattering
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