Opérateurs conjugués et propriétés de propagation. (French) Zbl 0543.47041

Mourre, E.

Commun. Math. Phys. 91, 279-300 (1983).

A self-adjoint operator A on a Hilbert space is said to be conjugate to another one, H, if \(Dom A\cap Dom H\) is a core for H and if \(e^{iA\alpha}\) leaves Dom H invariant, and, in addition \(\sup \| He^{iA\alpha}\psi \|<\infty \forall \psi \in Dom H.\) Several criteria and estimates concerning this notion are derived. Applications to the quantum-mechanical 3- and N-body problem (where the interaction is given through long range two body potentials) are given, notably to the singular central support of the Green’s functions.

Reviewer: A.Wehrl

MSC:

47L90	Applications of operator algebras to the sciences
47D03	Groups and semigroups of linear operators
46N99	Miscellaneous applications of functional analysis
81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81U10	\(n\)-body potential quantum scattering theory

Keywords:

conjugate operators; core; quantum-mechanical 3- and N-body problem; long range two body potentials; singular central support; Green’s functions

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