Abstract
The quantum -body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form , 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 the -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 -dependent term grows faster with increasing than the -independent term. Then, it is argued that such a behavior should also be observed with generic potentials and for -dimensional systems. Consequently, quantum -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