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arXiv · 2507.01002

SPARSE: Scattering Poles and Amplitudes from Radial Schrödinger Equations

Roberto Bruschini
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Abstract

We introduce an algorithm for the solution of a system of radial Schrödinger equations describing the inelastic scattering of particles with spin in a partial wave with definite total angular momentum. The system of differential equations is approximated as an ordinary linear nonhomogeneous system using the finite difference method. Dirichlet boundary conditions are imposed at the origin and at an arbitrary large radius. The numerical wavefunction is calculated using LAPACK general banded LU decomposition routines. The $K$-matrix for physical energies is calculated from the numerical solutions of the system by least-square fit to the analytical real solutions at large distances. The scattering amplitudes for physical energies is then calculated from the $K$-matrix. Scattering poles in the lower half of the unphysical Riemann sheet are calculated by numerical extrapolation of the scattering amplitudes using the AAA algorithm for rational approximation.

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Roberto Bruschini. 2026-09-15. SPARSE: Scattering Poles and Amplitudes from Radial Schrödinger Equations. https://arxiv.org/abs/2507.01002

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