Contracted Schrodinger equation connected equations

To complete our discussion of the formulas for the connected 3-RDM, we mention that the system of equations in Eq. (48) and the formula in Eq. (49), which is often called the Mazziotti correction [24, 26, 29] to distinguish it from the Nakatsuji-Yasuda correction [19, 24] for the 3-RDM, can also be derived from a contracted Schrodinger equation for the number operator ... 

CUMULANTS, EXTENSIVITY, AND THE CONNECTED FORMULATION OF THE CONTRACTED SCHRODINGER EQUATION... 

Formulating conditions for the energy to be stationary with respect to variations of the wavefunction P in this generalized normal ordering, one is led to the irreducible Brillouin conditions and irreducible contracted Schrodinger equations, which are conditions on the one-particle density matrix and the fe-particle cumulants k, and which differ from their traditional counterparts (even after reconstruction [4]) in being strictly separable (size consistent) and describable in terms of connected diagrams only. 

As mentioned in Section I, Cho [13], Cohen and Frishberg [14, 15], and Nakatsuji [16] integrated the Schrodinger equation and obtained an equation that they called the density equation. This equation was at the time also studied by Schlosser [44] for the 1-TRDM. In 1986 Valdemoro [17] applied a contracting mapping to the matrix representation of the Schrodinger equation and obtained the contracted Schrodinger equation (CSE). In 1986, at the Coleman Symposium where the CSE was first reported, Lowdin asked whether there was a connection between the CSE and the Nakatsuji s density equation. It came out that both... 

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