Lower bounds for the first n eigenvalues of the first order density matrix corresponding to a quantum mechanical state of an n-electron 6ystem are derived under the three assumptions:1. that one knows a lower bound to the overlap integral of an arbitrary normalized Slater determinant with the true wave function. 2. that the configuration interaction expansion of the true wave function contains only singly, doubly etc. up to m-fold excited configurations with respect to a 'ground' configuration, where 3. that the electronic interaction term in the Hamiltonian is proportional to a parameter λ and that a perturbation expansion in terms of this parameter is possible. In the latter case one finds that the idem potency of the one particle density matrix is stable with respect to first order perturbations.
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