Physics – Mathematical Physics
Scientific paper
2001-05-21
Physics
Mathematical Physics
Scientific paper
This work reviews recent advances in the analytical treatment of the continuum spectrum of correlated few-body non-relativistic Coulomb systems. The exactly solvable two-body problem serves as an introduction to the non-separable three-particle system. For the latter case we discuss the existence of an approximate separability of the long and the short-range dynamics which is exposed in an appropriately chosen curvilinear coordinates. The three-body wave functions of the long-ranged part of the Hamiltonian are derived and methods are presented to account approximately for the short-ranged dynamics. Furthermore, we present a generalization of the methods employed for the derivation of the three-body wave functions to the scattering states of $N$ charged particles. To deal with thermodynamic properties of finite systems we develop and discuss a recent Green function methodology designed for the non-perturbative regime. In addition, we give a brief account on how thermodynamic properties and critical phenomena can be exposed in finite interacting systems.
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