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

Abstract

I obtain the exact ground state of $N$-fermions in $D$-dimensions $(D\ge 2)$ 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.

10 pages, Latex file

References in corpus (4)

• Novel correlations in two dimensions: Some exact solutions
• A Quantum Many-body Problem in Two Dimensions: Ground State
• Novel correlations in two dimensions: Two-body problem
• Asymptotic analysis and spectrum of three anyons

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• Supersymmetry and Models for Two Kinds of Interacting Particles
• Exactly solvable model of three interacting particles in an external magnetic field
• Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems
• 2D Calogero Model in the Collective-Field Approach
• Parent Hamiltonians of Jastrow Wavefunctions