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Asymptotic properties of generalized eigenfunctions for three body Schrödinger operators. (English) Zbl 0774.35064
Continuing his previous work [Commun. Math. Phys. 146, No. 2, 241-258 (1992; Zbl 0748.35026)], the author considers the generalized eigenfunctions of the Schrödinger operator for three particles with binary interactions. He proves that the large-distance asymptotic behavior of those generalized eigenfunctions that describe an initial state of two clusters agrees with that derived by less rigorous arguments by R. G. Newton [Ann. Phys. 74, 324-351 (1972)]. He thereby rigorously derives expressions for elements of the \(S\) matrix that correspond to the collision of a particle with a bound state of two others.

MSC:
35Q40 PDEs in connection with quantum mechanics
35P25 Scattering theory for PDEs
47A40 Scattering theory of linear operators
81U10 \(n\)-body potential quantum scattering theory
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