Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9712133 · Journal of Mathematical Physics

Exact ground state of several N-body problems with an N-body potential

Avinash Khare

Published Jun 1, 1999• 3 citations
arXivHTMLPDF

Abstract

The exact (bosonic) ground state and a class of excited states are obtained for several Calogero-type N-body problems in D dimensions when the N bodies are also interacting via an N-body potential of the form −e2/Σri2.
DOI
10.1063/1.532720

Related papers

N Fermion Ground State of Calogero-Sutherland type Models in Two and Higher Dimensions

Avinash Khare

I obtain the exact ground state of N-fermions in D-dimensions (D ≥ 2) in case the N particles are interacting via long-ranged two-body and three-body interactions and further they are also interacting via the harmonic oscillator potential. I also obtain the N-fermion ground state in case the oscillator potential is replaced by an N-body Coulomb-like interaction.

•Jan 1, 1998•5 citations

Novel Correlations in Two Dimensions: Some Exact Solutions

M. V. N. Murthy, R. K. Bhaduri, Diptiman Sen

We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring.

arXiv:cond-mat/9603155•Physical Review Letters•May 27, 1996•31 citations

Exact Solution For a Class of Calogero-Sutherland Type N-body Problems

Avinash Khare

•Jan 1, 1999•0 citations

Quantum Many-Body Problem in One Dimension: Ground State

Bill Sutherland

We investigate the ground state of a system of either fermions or bosons interacting in one dimension by a 2‐body potential V(r) = g/r2. In the thermodynamic limit, we determine the ground state energy and pair correlation function.

Advanced series in mathematical physics•May 1, 1994•0 citations

Quantum Many-Body Problem in One Dimension: Ground State

Bill Sutherland

We investigate the ground state of a system of either fermions or bosons interacting in one dimension by a 2-body potential V(r) = g/r2. In the thermodynamic limit, we determine the ground state energy and pair correlation function.

Journal of Mathematical Physics•Feb 1, 1971•696 citations

Comparison between the exact and Hartree solutions of a one-dimensional many-body problem

Francesco Calogero, A. Degasperis

The exact solution for the ground state of the quantum one-dimensional $N$-boson problem with attractive $\ensuremath{\delta}$-function two-body potentials is compared with the (exact) self-consistent solution of the corresponding variational Hartree problem.

Physical Review A•Jan 1, 1975•136 citations
We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring.
The exact solution for the ground state of the quantum one-dimensional NNN-boson problem with attractive $\ensuremath{\delta}$-function two-body potentials is compared with the (exact) self-consistent solution of the corresponding variational Hartree problem.