Coordinate space representation of a one-dimensional odd-parity pseudopotential
Abstract
We propose a discrete-space representation of a one-dimensional zero-range odd-parity pseudopotential. The proposed representation is validated by applying it to the analytically solvable case of two fermions in a harmonic trap and successfully recovering the exact energy spectrum and eigenfunctions. Furthermore, we use the square-well and modified P\"oschl--Teller potentials as finite-range representations of the odd-parity interaction and study their convergence to the contact interaction when the range tends to zero. Finally, we perform natural orbital analysis and compute the eigenvalues of the one-body density matrix for different particle numbers, examining their dependence on the one-dimensional scattering length and identifying distinct physical regimes.
Cite
@article{arxiv.2509.01995,
title = {Coordinate space representation of a one-dimensional odd-parity pseudopotential},
author = {Marc Camus-Sais and Abel Rojo-Francàs and Grigori E. Astrakharchik and Bruno Juliá-Díaz},
journal= {arXiv preprint arXiv:2509.01995},
year = {2026}
}