1997/01/01 by V. S. Vasilevsky, F. Arickx · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Simulation and Numerical Methods #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics #nucl-th
paper · pdf · doi:10.1103/physreva.55.265
published as Phys. Rev. A 55 (1997) 265 · 31 pages, 41 postscript figures
openalex publication_date 1997/01/01 · arxiv created 2000/05/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The convergence problem for scattering states is studied in detail within the framework of the algebraic model, a representation of the Schr"odinger 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 nonoptimal bases is formulated based on the asymptotic behavior of the dynamical coefficients. These strategies are shown to provide a dramatically improved convergence of the solutions.