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- W2057097893 abstract "The quantum mechanics of n particles interacting through analytic two-body interactions can be formulated as a problem of functional analysis on a Hilbert space G consisting of analytic functions. On G, there is an Hamiltonian H with resolvent R(λ). These quantities are associated with families of operators H(ϑ) and R(λ, ϑ) on L, the case ϑ = 0 corresponding to standard quantum mechanics. The spectrum of H(ϑ) consists of possible isolated points, plus a number of half-lines starting at the thresholds of scattering channels and making an angle 2ϑ with the real axis. Assuming that the two-body interactions are in the Schmidt class on the two-particle space G, this paper studies the resolvent R(λ, ϑ) in the case ϑ ≠ 0. It is shown that a well known Fredholm equation for R(λ, ϑ) can be solved by the Neumann series whenever ¦λ¦ is sufficiently large and λ is not on a singular half-line. Owing to this, R(λ, ϑ) can be integrated around the various half-lines to yield bounded idempotent operators Pp(ϑ) (p = 1, 2,…) on L. The range of Pp(ϑ) is an invariant subspace of H(ϑ). As ϑ varies, the family of operators Pp(ϑ) generates a bounded idempotent operator Pp on a space G. The range of this is an invariant subspace of H. The relevance of this result to the problem of asymptotic completeness is indicated." @default.
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- W2057097893 date "1975-01-01" @default.
- W2057097893 modified "2023-10-16" @default.
- W2057097893 title "Invariant subspaces of analytic multiparticle Hamiltonians" @default.
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- W2057097893 doi "https://doi.org/10.1016/0022-247x(75)90163-8" @default.
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