Efficient determination of eigenenergies and eigenstates of $N$ ($N=3$--$4$) identical 1D bosons and fermions under external harmonic confinement

• URL: http://arxiv.org/abs/2509.02938v1
• Date: Wed, 03 Sep 2025 02:06:40 GMT
• Title: Efficient determination of eigenenergies and eigenstates of $N$ ($N=3$--$4$) identical 1D bosons and fermions under external harmonic confinement
• Authors: J. D. Norris, D. Blume,
• Abstract summary: This work introduces a new approach for determining the energy spectra and eigenstates of small harmonically trapped single-component Bose and Fermi gases with additive two-body zero-range interactions in one spatial dimension.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Few-atom systems play an important role in understanding the transition from few- to many-body quantum behaviors. This work introduces a new approach for determining the energy spectra and eigenstates of small harmonically trapped single-component Bose and Fermi gases with additive two-body zero-range interactions in one spatial dimension. The interactions for bosons are the usual $\delta$-function interactions while those for fermions are $\delta$-function interactions that contain derivative operators. Details of the derivation and benchmarks of the numerical scheme are presented. Extensions to other systems are discussed.

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