Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-11-16
Phys.Rev.82:062102,2010
Physics
High Energy Physics
High Energy Physics - Theory
To appear in PRA
Scientific paper
10.1103/PhysRevA.82.062102
The quantum $N$-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form $[\hat x,\hat p]=i(1+\beta \hat p^2)$, leading to the existence of a minimal observable length $\sqrt\beta$. For a generic pairwise interaction potential, analytical formulas are obtained that allow to estimate 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 $\beta$-dependent term grows faster with $N$ than the $\beta$-independent one. Then, it is argued that such a behavior should be observed also with generic potentials and for $D$-dimensional systems. In consequence, quantum $N$-body bound states might be interesting places to look at nontrivial manifestations of a minimal length since, the more particles are present, the more the system deviates from standard quantum mechanical predictions.
No associations
LandOfFree
The quantum N-body problem with a minimal length does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The quantum N-body problem with a minimal length, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The quantum N-body problem with a minimal length will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-464511