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

TL;DR

This paper derives exact ground states for N-fermion systems in higher dimensions with long-range interactions, including harmonic and Coulomb-like potentials, expanding understanding of complex many-body quantum states.

Contribution

It provides explicit solutions for the ground states of N-fermions in D-dimensional systems with long-range two- and three-body interactions, including harmonic and Coulomb-like potentials.

Findings

Exact ground state solutions for N-fermions in D ≥ 2 dimensions.

Inclusion of long-range two- and three-body interactions.

Ground states for both harmonic oscillator and Coulomb-like potentials.

Abstract

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