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Isozaki, Hiroshi

Structures of S-matrices for three body Schrödinger operators. (English) Zbl 0748.35026

Commun. Math. Phys. 146, No. 2, 241-258 (1992).
Summary: Structures of the \(S\)-matrix associated with the collision process from 2 clusters to 3 clusters are studied. This \(S\)-matrix is shown to have a continuous kernel except for 2-dimensional spheres on which 2-body subsystems have zero velocity. On these spheres, the \(S\)-matrix has, in general, singularities whose existence arises from the zero eigenvalues and the zero resonances of the 2-body subsystems.

Cited in 1 Review
Cited in 12 Documents

MSC:

35P25 Scattering theory for PDEs
81U20 \(S\)-matrix theory, etc. in quantum theory
35Q40 PDEs in connection with quantum mechanics
47A40 Scattering theory of linear operators
81U10 \(n\)-body potential quantum scattering theory

Keywords:

collision process; continuous kernel; singularities
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\textit{H. Isozaki}, Commun. Math. Phys. 146, No. 2, 241--258 (1992; Zbl 0748.35026)
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References:

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