ALGEBRAIC MODEL FOR QUANTUM SCATTERING - REFORMULATION, ANALYSIS, ANDNUMERICAL STRATEGIES

The convergence problem for scattering states is studied in detail wit hin the framework of the algebraic model, a representation of the Schr odinger equation in an L(2) basis. The dynamical equations of this mod el are reformulated featuring new ''dynamical coefficients,'' which ex plicitly reveal the potential effects. A general analysis of the dynam ical coefficients leads to an optimal basis yielding well converging, precise, and stable results. A set of strategies for solving the equat ions for nonoptimal bases is formulated based on the asymptotic behavi or of the dynamical coefficients. These strategies are shown to provid e a dramatically improved convergence of the solutions.