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On the discrete spectrum of theN-body quantum mechanical hamiltonian. I

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Abstract

We discussN-body kinematics and study the Berezin-Sigal equations in configuration space. Assuming that the threshold of the continuous spectrum is zero and that the pair potentials satisfy |V(x)|≦C(1+|x|2)−Q, ϰ ∈ ℝ3 ϱ > 1 (together with some technical hypotheses), we show that the discrete spectrum of the hamiltonian in the center of mass system is finite. The case of negative threshold will be treated in a further publication.

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Authors and Affiliations

  1. Departmento de Matematica, Pontificia Universidade Católica, Rio de Janeiro, Brasil

    Rafael Jose Iorio Jr.

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  1. Rafael Jose Iorio Jr.
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Additional information

Communicated by J. Ginibre

This work was done while the author was staying at U.C. Berkeley and was partially supported by Pontificia Universidade Católica and by the Brazilian National Research Council (CNPq)

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Iorio, R.J. On the discrete spectrum of theN-body quantum mechanical hamiltonian. I. Commun.Math. Phys. 62, 201–212 (1978). https://doi.org/10.1007/BF01202524

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