Quantum $N$-body problem: Matrix structures and equations

We consider matrix structures in the quantum $N$-body problem that generalize the Faddeev components for resolvents, $T$-matrices, and eigenfunctions of the continuous spectrum. We write matrix equations for the introduced components of $T$-matrices and resolvents and use these equations to obtain matrix operators generalizing the matrix three-particle Faddeev operators to the case of arbitrarily many particles. We determine the eigenfunctions of the continuous spectrum of these matrix operators.