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Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions

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Abstract

Quantum mechanicalN-body systems with dilatation analytic interactions are investigated. Absence of continuous singular part for the Hamiltonians is proved together with the existence of an absolutely continuous part having spectrum [λ e , ∞), where λ e is the lowest many body threshold of the system. In the complement of the set of thresholds the point spectrum is discrete; corresponding bound state wave-functions are analytic with respect to the dilatation group.

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Authors and Affiliations

  1. Department of Mathematics, SUNY at Buffalo, New York, USA

    E. Balslev

  2. Centre de Physique Théorique — C.N.R.S., Marseille, France

    J. M. Combes

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  1. E. Balslev
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  2. J. M. Combes
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Balslev, E., Combes, J.M. Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions. Commun.Math. Phys. 22, 280–294 (1971). https://doi.org/10.1007/BF01877511

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  • DOI: https://doi.org/10.1007/BF01877511

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