Spinless Bosons or Spin 1/2 Fermions in a 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction I - General Theory

TL;DR

This paper develops a general theoretical framework for analyzing large systems of 1D trapped spinless bosons or spin-1/2 fermions with repulsive delta interactions, providing insights into their many-body behavior.

Contribution

It introduces a comprehensive theoretical approach to solve the many-body problem for large N in 1D harmonic traps with delta interactions, applicable to both bosons and fermions.

Findings

Solution for large N limit of 1D trapped particles

Unified treatment for bosons and fermions with delta interactions

Foundational basis for further many-body analysis

Abstract

In these two papers, we solve the N body 1D harmonically trapped spinless Boson or spin 1/2 Fermions with repulsive delta function interaction in the limit $N\to \infty$.