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.
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