On the finiteness of discrete spectrum in the n-particle problem. (English) Zbl 0581.46063

Vugal’ter, S. A.; Zhislin, G. M.

Rep. Math. Phys. 19, 39-90 (1984).

Authors’ summary: ”In spaces of functions of any given symmetry, sufficient conditions have been obtained for the discrete spectrum finiteness of the energy operators of many particle quantum systems in the absence of external fields.
The most general case is considered when the beginning of the essential spectrum of the Hamiltonian is defind by breaking the initial system into any number of stable subsystems. Results obtained are applicable in particular to systems with a short-range and to systems with long-range action (in the case of interaction compensation).”

Reviewer: P.Hillion

MSC:

46N99	Miscellaneous applications of functional analysis
47A70	(Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
47A40	Scattering theory of linear operators
81U10	\(n\)-body potential quantum scattering theory

Keywords:

m-particle problem; discrete spectrum; many particle Hamiltonain; energy operator; discrete spectrum finiteness of the energy operators of many particle quantum systems in the absence of external fields; essential spectrum of the Hamiltonian; breaking the initial system into any number of stable subsystems; systems with long-range action

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