Algebraic Model for Quantum Scattering. Reformulation, Analysis and Numerical Strategies

Details Algebraic Model for Quantum Scattering. Reformulation, Analysis and Numerical Strategies Algebraic Model for Quantum Scattering. Reformulation, Analysis and Numerical Strategies

2000-05-17

arxiv.org/abs/nucl-th/0005048v1

Phys. Rev. A 55 (1997) 265

Physics

Nuclear Physics

Nuclear Theory

31 pages, 41 postscript figures

Scientific paper

10.1103/PhysRevA.55.265

The convergence problem for scattering states is studied in detail within the framework of the Algebraic Model, a representation of the Schrodinger equation in an L^2 basis. The dynamical equations of this model are reformulated featuring new "Dynamical Coefficients", which explicitly reveal the potential effects. A general analysis of the Dynamical Coefficients leads to an optimal basis yielding well converging, precise and stable results. A set of strategies for solving the equations for non-optimal bases is formulated based on the asymptotic behaviour of the Dynamical Coefficients. These strategies are shown to provide a dramatically improved convergence of the solutions.

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