Schrodinger equation contracted

ORBITAL REPRESENTATION OE THE CONTRACTED SCHRODINGER EQUATION (CSchE)... 

F. Colmenero and C. Valdemoro, Self-consistent approximate solution of the 2nd-order contracted Schrodinger equation. Int. J. Quantum Chem. 51, 369 (1994). 

C. Valdemoro, L. M. Tel, and E. Perez-Romero, The contracted Schrodinger equation some results. Adv. Quantum Chem. 28, 33 (1997). 

D. A. Mazziotti, Contracted Schrodinger equation determining quantum energies and two-particle density matrices without wave functions. Phys. Rev. A 57, 4219 (1998). 

D. A. Mazziotti, Solution of the 1,3-contracted Schrodinger equation through positivity conditions on the 2-particle reduced density matrix. Phys. Rev. A 66, 062503 (2002). 

We have focused on the lower bound method, but density matrix research has moved forward on a much broader front than that. In particular, work on the contracted Schrodinger equation played an important role in developments. A more complete picture can be found in Coleman and Yukalov s book [23]. It has taken 55 years and work by many scientists to fulfill Coleman s 1951 claim at Chalk River that except for a few details which would be easily overcome in a couple of weeks—the A-body problem has been reduced to a 2.5-body problem ... 

Properties of the 2-RDM and the V-Representability Ih-oblem The Matrix Contracting Mapping The Contracted Schrodinger Equation... 

Iterative Solution of the Contracted Schrodinger Equation The Reduced Density Matrices Construction Algorithms A. The 2-RDM Construction Algorithm... 

VI. An Exact Formal Solution to the Contracted Schrodinger Equation s Indeterminacy... 

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... 

VI. AN EXACT FORMAL SOLUTION TO THE CONTRACTED SCHRODINGER EQUATION S INDETERMINACY... 

The outlook given in this chapter on the theory of the second-order contracted Schrodinger equation and on its methodology has been aimed mostly at convincing the reader that this theory is not difficult to understand and that its methodology is now ready to be applied. That is, in the author s opinion, this methodology can be considered as accurate and probably more economical than the best standard quantum chemical computational methods for the study of states where the occupation number of spin orbitals is close to one or zero. 

D. R. Alcoba and C. Valdemoro, Family of modified-contracted Schrodinger equations. Phys. Rev. A 64, 062105 (2001). 

D. R. Alcoba, Equivalence theorems between the solutions of the fourth-order modified contracted Schrodinger equation and those of the Schrodinger equation. Phys. Rev. A 65, 032519 (2002). 

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 ... 

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