### Abstract

A full strength Coulomb interaction between trapped electrons can be
felt only in absence of a neutralizing background. In order to study
quantum degenerate electrons without such a background, an external trap
is needed to compensate for the strong electronic repulsion. As a basic
model for such a system, we study a trapped electron pair in a harmonic
trap with an explicit inclusion of its Coulomb interaction. We find the
eigenenergy of the ground state, confirming earlier work in the context
of harmonium. We extend this to a complete set of properly scaled
energies for any value of the trapping strength, including the excited
states. The problem is solved either numerically or by making harmonic
approximations to the potential. As function of the trapping strength a
crossover can be made from the strongly to the weakly-coupled regime,
and we show that in both regimes perturbative methods based on a
pair-wise electron description would be effective for a many-particle
trapped electron system, which resembles a Wigner crystal in the ground
state of the strongly coupled limit.

Original language | English |
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Article number | 1508.00365 |

Number of pages | 6 |

Journal | arXiv.org, e-Print Archive, Physics |

Volume | 2015 |

Publication status | Published - 1 Aug 2015 |

### Keywords

- Condensed Matter - Quantum Gases
- Quantum Physics

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## Cite this

Kroeze, R., Luiten, J., & Kokkelmans, S. (2015). Trapped electrons in the quantum degenerate regime.

*arXiv.org, e-Print Archive, Physics*,*2015*, [1508.00365]. https://arxiv.org/abs/1508.00365