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arXiv · 1501.02531

Wave-packet continuum discretization for quantum scattering

O. A. Rubtsova·V. I. Kukulin·V. N. Pomerantsev
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Abstract

A general approach to a solution of few- and many-body scattering problems based on a continuum-discretization procedure is described in detail. The complete discretization of continuous spectrum is realized using stationary wave packets which are the normalized states constructed from exact non-normalized continuum states. Projecting the wave functions and all scattering operators like $t$-matrix, resolvent, etc. on such a wave-packet basis results in a formulation of quantum scattering problem entirely in terms of discrete elements and linear equations with regular matrices. It is demonstrated that there is a close relation between the above stationary wave packets and pseudostates which are employed often to approximate the scattering states with a finite $L_2$ basis. Such a fully discrete treatment of complicated few- and many-body scattering problems leads to significant simplification of their practical solution. Also we get finite-dimensional approximations for complicated operators like effective interactions between composite particles constructed via the Feshbach-type projection formalism. As illustrations to this general approach we consider several important particular problems including multichannel scattering and scattering in the three-nucleon system within the Faddeev framework.

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O. A. Rubtsova, V. I. Kukulin, V. N. Pomerantsev. 2015-01-15. Wave-packet continuum discretization for quantum scattering. https://arxiv.org/abs/1501.02531

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