### Abstract

The model considered here is the "jellium" model in which there is a uniform, fixed background with charge density - eρ in a large volume V and in which N = ρV particles of electric charge +e and mass m move - the whole system being neutral. In 1961 Foldy used Bogolubov's 1947 method to investigate the ground state energy of this system for bosonic particles in the large ρ limit. He found that the energy per particle is - 0.402r^{-3/4}_{s} me^{4}/ℏ^{2} in this limit, where r_{s} = (3/4πρ)^{1/3}e^{2}m/ℏ^{2}. Here we prove that this formula is correct, thereby validating, for the first time, at least one aspect of Bogolubov's pairing theory of the Bose gas.

Original language | English (US) |
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Pages (from-to) | 127-163 |

Number of pages | 37 |

Journal | Communications In Mathematical Physics |

Volume | 217 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2001 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Lieb, E. H., & Solovej, J. P. (2001). Ground state energy of the one-component charged Bose gas.

*Communications In Mathematical Physics*,*217*(1), 127-163. https://doi.org/10.1007/s002200000353