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

V. S. Vasilevsky·F. Arickx
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Abstract

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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V. S. Vasilevsky, F. Arickx. 2000-05-17. Algebraic Model for Quantum Scattering. Reformulation, Analysis and Numerical Strategies. https://doi.org/10.1103/physreva.55.265

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