Generalizations of the Fock and Kato expansions to systems of three quantum particles

The Schrodinger and Faddeev approaches to the solution of the problem of three quantum particles in the configuration space are used and developed in this review. Various methods for construction of generalizations of the Fock and Kato expansions to central or noncentral pair interactions of a more general type than Coulomb potentials are described and compared within the approaches in question. Emphasis is placed on the use of these generalizations for quantum-mechanical and numerical analysis of the structure of three-body wave functions and their Faddeev components near the two-body and three-body collision points and in the limit of the linear three-body configuration.