Schrodinger equation direct variational solution

The question, what conditions are to be fulfilled by a density matrix to be the image of a wave function, that is, to describe a real physical system is opened till today. The contracted Schrodinger-equations derived for different order reduced density matrices by H. Nakatsui [1] give opportunity to determine density matrices by a non-variational way. The equations contain density matrices of different order, and the relationships needed for the exact solutions are not yet known in spite of the intensive research activity [2,3]. Recently perturbation theory corrections were published for correcting the error of the energy obtained by minimizing the density matrix directly applying the known conditions of N-representability [4], and... 

The idea of using functions of the form frjr for approximate solutions of the boundary value problems has been used in a large number of papers. For example, this idea was used in [70] for the one-dimensional Schrodinger equation to prove the Hull-Julius relation (4.21) and to study the confined IlJ molecule. The direct use of the Kirkwood-Buckingham relation for variational calculations of the hydrogen atom in a half space was... 

The ifirst solvent term, V/ does not lead to any difficulty, neither from the theoretical point of view, neither from the practical. Many examples are known in which an external potential is introduced in the molecular calculations. On the contrary, the treatment of the reaction potential operator prV , ( 1 pr> 1 ) is rather delicate, as this term induces a nonlinear character to the solute Schrodinger equation. We recall that the nonlinear eq. (1.2) is a direct consequence of the variational principle applied to G-The free energy functional G has a privileged role in the theory, as the... 

Direct Variational Method for Schrodinger Equation Solution... 

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