Natural Expansion of a Many-Electron Wave Function

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Abstract
It is shown that the validity of the natural expansion of a many-electron wave function can be established through extremum conditions applied to the diagonal elements of the pure-state density operator constructed from the state vector of the system in a tensor-product space of rank two. From this viewpoint, a variational definition of the two complementary reduced density operators can be given, and deductions can be drawn concerning the properties of the reduced density operators. It is therefore advantageous to regard the related expressions and many of the analytical properties of the reduced density matrices as arising from the solution of a two-space variational problem. A practical method of obtaining this expansion from a wave function of arbitrary form is developed. Functional equations analogous to this type of expansion in a tensor-product space of higher rank and with constraints of pairwise orthogonality are also derived.