### Abstract

The quantum-mechanical, fermion, attractive delta function gas in one dimension has many interesting, known physical properties, including some aspects of soliton behavior. Motivated by a desire to test the validity of the HF approximation to many-body systems, we have made a rigorous study of the HF theory of this gas. When the particle number is even we can show that although HF theory does not give energies accurately, it does correctly predict the known qualitative properties; in particular, only two-particle bound states exist.

Original language | English (US) |
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Pages (from-to) | 860-868 |

Number of pages | 9 |

Journal | Journal of Mathematical Physics |

Volume | 19 |

Issue number | 4 |

DOIs | |

State | Published - 1977 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Lieb, E. H., & De Llano, M. (1977). Solitons and the delta function fermion gas in Hartree-Fock theory.

*Journal of Mathematical Physics*,*19*(4), 860-868. https://doi.org/10.1063/1.523748