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Exactly Solvable \({\varvec{N}}\)-Body Quantum Systems with \(\varvec{N=3^k \ ( k}\) \(\ge \) \(\varvec{2)}\) in the \({\varvec{D=1}}\) Dimensional Space

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Abstract

We study the exact solutions of a particular class of N confined particles of equal mass, with \(N=3^k \ (k=2,3, \ldots ),\) in the \(D=1\) dimensional space. The particles are clustered in clusters of three particles. The interactions involve a confining mean field, two-body Calogero type of potentials inside the cluster, interactions between the centres of mass of the clusters and finally a non-translationally invariant N-body potential. The case of nine particles is exactly solved, in a first step, by providing the full eigensolutions and eigenenergies. Extending this procedure, the general case of N particles (\(N=3^k, \ k \ge 2\)) is studied in a second step. The exact solutions are obtained via appropriate coordinate transformations and separation of variables. The eigenwave functions and the corresponding energy spectrum are provided.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Département de Physique, Université Mentouri, Constantine, Algeria

    A. Bachkhaznadji

  2. Institut de Physique Nucléaire, CNRS-IN2P3, Université Paris-Sud, Université Paris-Saclay, 91406, Orsay Cedex, France

    M. Lassaut

Authors
  1. A. Bachkhaznadji
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  2. M. Lassaut
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Correspondence to M. Lassaut.

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Bachkhaznadji, A., Lassaut, M. Exactly Solvable \({\varvec{N}}\)-Body Quantum Systems with \(\varvec{N=3^k \ ( k}\) \(\ge \) \(\varvec{2)}\) in the \({\varvec{D=1}}\) Dimensional Space. Few-Body Syst 57, 773–791 (2016). https://doi.org/10.1007/s00601-016-1107-z

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  • DOI: https://doi.org/10.1007/s00601-016-1107-z

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