Quantum N-body problem with a minimal length

Fabien Buisseret
Phys. Rev. A 82, 062102 – Published 6 December 2010

Abstract

The quantum N-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form [,]=i(1+β2), leading to the existence of a minimal observable length β. For a generic pairwise interaction potential, analytical formulas are obtained that allow estimation of the ground-state energy of the N-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 β-dependent term grows faster with increasing N than the β-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.

  • Received 8 September 2010

DOI:https://doi.org/10.1103/PhysRevA.82.062102

© 2010 The American Physical Society

Authors & Affiliations

Fabien Buisseret*

  • Service de Physique Nucléaire et Subnucléaire, Université de Mons–UMONS, Académie universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons, Belgium

  • *fabien.buisseret@umons.ac.be

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Vol. 82, Iss. 6 — December 2010

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