Modified contracted Schrodinger equations

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). 

Another extension of this theoretical smdy is the consideration of both an economical and an effective purification strategy for the 4-RDM. The need for such a purification scheme is motivated by the need to have an N- and 5-representable 4-RDM if one wishes to solve the fourth-order modified contracted Schrodinger equation [62, 64, 87]. There have already been several attemps to purify both the 3-RDM and 4-RDM [18, 34, 52]. In particular, a set of inequalities that bound the diagonal and off-diagonal elements of these high-order matrices have been reported [18]. However, the results obtained with this approach within the framework of the fourth-order modified contracted Schrodinger equation (and the second-order contracted Schrodinger equation) were not fully satisfactory because the different spin-blocks of the matrices did not appear to be properly balanced [87, 114]. 

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