Exactly solvable N-body quantum systems with N=3k (k≥2) in the D=1 dimensional space

Abstract : We study the exact solutions of a particular class of N confined particles of equal mass, with N=3k (k=2,3,...), in the D=1 dimensional space. The particles are clustered in clusters of 3 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 9 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=3k, k≥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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http://hal.in2p3.fr/in2p3-01411251
Contributor : Sophie Heurteau <>
Submitted on : Wednesday, December 7, 2016 - 11:51:40 AM
Last modification on : Thursday, January 11, 2018 - 6:12:40 AM

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  • HAL Id : in2p3-01411251, version 1
  • ARXIV : 1608.08479

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A. Bachkhaznadji, M. Lassaut. Exactly solvable N-body quantum systems with N=3k (k≥2) in the D=1 dimensional space. 2016. ⟨in2p3-01411251⟩

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