Equivalence theorems between the solutions of the fourth-order modified contracted Schrodinger equation and those of the Schrodinger equation

Four basic theorems involving the correlation matrices are demonstrated here. One of these theorems establishes, as a necessary and sufficient condition, that the solutions of the fourth-order modified contracted Schrodinger equation correspond uniquely to those of the Schrodinger equation. The complete equivalence between these two equations is demonstrated. Another equation equivalent to the Schrodinger equation but involving only the correlation matrices is also obtained as a consequence of the second theorem.