The quantum N-body problem with a minimal length

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

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

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

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.

Rate now

     

Profile ID: LFWR-SCP-O-464511

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.