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2010-12-06 - Article/Dans un journal avec peer-review - Anglais - 4 page(s)

Buisseret Fabien , "Quantum N-body problem with a minimal length" in Physical Review. A, 82, 062102/1-4

  • Edition : American Physical Society, College Park (MD)
  • Codes CREF : Physique théorique et mathématique (DI1210), Mécanique quantique classique et relativiste (DI1211)
  • Unités de recherche UMONS : Physique nucléaire et subnucléaire (S824)
Texte intégral :

Abstract(s) :

(Anglais) The quantum N-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form [x,p] = i(1 +ß p²), leading to the existence of a minimal observable length. For a generic pairwise interaction potential, analytical formulas are obtained that allow estimation of the ground-state energy of theN-body system by finding the ground-state energy of a corresponding two-body problem. It is first shown that in the harmonic oscillator case, the ß-dependent term grows faster with increasing N than the ß-independent term. Then, it is argued that such a behavior should also be observed with generic potentials and for D-dimensional systems. Consequently, quantum N-body bound states might be interesting places to look at nontrivial manifestations of a minimal length, since the more particles that are present, the more the system deviates from standard quantum-mechanical predictions

Identifiants :
  • DOI : 10.1103/PhysRevA.82.062102
  • arXiv : 1011.3690