### Abstract

The following question is considered: What special properties are possessed by those reduced density matrices which come from energy eigenstates? Using the fact that 〈φ[H, A] |φ〉 = 0, where A is any operator and |φ〉 an energy eigenstate, it is shown that the elements of the two-particle density matrix are severely restricted by homogeneous linear relations. Their full content is expressed in terms of an auxiliary one-particle density which possesses additional positivity properties in the ground state.

Original language | English (US) |
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Pages (from-to) | 1761-1763 |

Number of pages | 3 |

Journal | Journal of Mathematical Physics |

Volume | 10 |

Issue number | 9 |

DOIs | |

State | Published - 1969 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Rosina, M., Percus, J. K., Kijewski, L. J., & Garrod, C. (1969). Reduced density matrices of energy eigenstates.

*Journal of Mathematical Physics*,*10*(9), 1761-1763. https://doi.org/10.1063/1.1665024