Quantum scattering theory for several particle systems. Transl. from the Russian. (English) Zbl 0797.47005

Mathematical Physics and Applied Mathematics. 11. Dordrecht: Kluwer Academic Publishers. xiii, 404 p. (1993).
The intention of the book is to present the time-independent quantum mechanical scattering theory for \(N\)-particles. The kinematics and dynamics of \(N\)-body systems are described. In the whole book both short range and long range interactions are studied. Time-dependent wave and scattering operators are introduced and reformulated in a stationary way. The stationary wave operators are expressed by resolvent kernels or Green’s functions. Their principal singularities, i.e. poles and \(\delta\)-like singularities, are analyzed. Integral equations are useful means for the determination of the resolvent and for describing its singularities. Properties of Green’s functions imply the asymptotic completeness of the wave operators. For two particle systems this is based on the Fredholm theory. For three particles the system of Faddeev’s equations is established. For \(N\)-particles the Faddeev-Yakubowskij equation is described.
Another topic of the book is the study of wave functions and resolvent kernels for neutral and charged particles (i.e. short and long range interactions) in configuration space. In particular, they show that the wave functions can be found by solving, either the Schrödinger equation or differential equations for certain components of the Green function with some asymptotic boundary conditions. One main advantage of this differential formalism is to be effective for computational methods.
The book is written in a describing way for presenting the physical and mathematical problems. Several proofs are omitted. Almost every chapter has its own introduction. The list of references is restricted to the sources of the book. It gives a certain survey about the time-independent asymptotic completeness up to 1983.
[For the Russian original see Zbl 0585.35078].
Reviewer: M.Demuth (Potsdam)


47A40 Scattering theory of linear operators
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
35P25 Scattering theory for PDEs
81U10 \(n\)-body potential quantum scattering theory


Zbl 0585.35078