### Abstract

We continue the study of the integrodifferential equation proposed previously for the evaluation of the ground-state energy of an imperfect Bose gas. We apply it here to the one-dimensional delta-function gas where the exact result is known for all values of the coupling constant. The results are: (i) For small, the equation gives the correct first two terms in an asymptotic series; (ii) a numerical solution of the equation shows that the maximum relative error occurs for = in which case it is 19%; (iii) for = we are able to compare the exact two-particle distribution function with that given by the equation. The agreement is quite good.

Original language | English (US) |
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Journal | Physical Review |

Volume | 134 |

Issue number | 2A |

DOIs | |

State | Published - Dec 1 1964 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

Lieb, E., & Liniger, W. (1964). Simplified approach to the ground-state energy of an imperfect Bose gas. III. Application to the one-dimensional model.

*Physical Review*,*134*(2A). https://doi.org/10.1103/PhysRev.134.A312