Quantum Scattering Theory for Several Particle Systems

Dimitri R. Yafaev

L. D. Faddeev

S. Zienau

G. Bencze, C. Chandler

A time-dependent multichannel nonrelativistic quantum scattering theory is established for systems which contain identical particles. The symmetry properties of the theory are rooted in the abstract algebraic relationships between permutations. The formalism of second quantization is thus avoided. Appropriate wave and scattering operators are defined, including those for systems with long range (e.g., Coulomb) interactions. A correctly symmetrized dynamical equation for the symmetric form of the transition operator is derived and used to develop an optical potential formalism.NUCLEAR REACTIONS Nonrelativistic multichannel scattering theory for identical particles, wave and scattering operators, dynamical equations, optical potentials.

Dimitri R. Yafaev

The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding scattering matrix and illustrate them on the example of the Schrödinger equation. Our goal is to present time-dependent and stationary approaches and to describe the underlying mathematical methods. We also give a sketch of scattering theory for three interacting quantum particles including a difficult problem of the asymptotic completeness of scattering channels. Along with traditional results, we discuss new scattering channels arising for long-range pair interactions.

K. N. Joshipura, Nigel John Mason