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<p>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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-function interactions while those for fermions are <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-function interactions that contain derivative operators. Details of the derivation and benchmarks of the numerical scheme are presented. Extensions to other systems are discussed.</p>

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Efficient Determination of Eigenenergies and Eigenstates of N (\(N=3\)–4) Identical 1D Bosons and Fermions Under External Harmonic Confinement

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • J. D. Norris,
  • D. Blume

摘要

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 \(\delta \) δ -function interactions while those for fermions are \(\delta \) δ -function interactions that contain derivative operators. Details of the derivation and benchmarks of the numerical scheme are presented. Extensions to other systems are discussed.