Algebraic Model for Quantum Scattering. Reformulation, Analysis and Numerical Strategies
V. S. Vasilevsky, F. Arickx
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 L2 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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