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SPARSE: Scattering Poles and Amplitudes from Radial Schr\"odinger Equations
arXiv:2507.01002v4 Announce Type: replace Abstract: We introduce an algorithm for the solution of a system of radial Schr\"odinger 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.
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.
Quantum Physics (quant-ph); High Energy Physics - Phenomenology (hep-ph); Computational Physics (physics.comp-ph)
arXiv:2507.01002 [quant-ph]
(or arXiv:2507.01002v4 [quant-ph] for this version)
From: Roberto Bruschini Ph.D. [view email] [v1] Tue, 1 Jul 2025 17:53:05 UTC (141 KB) [v2] Wed, 26 Nov 2025 09:41:16 UTC (131 KB) [v3] Mon, 16 Mar 2026 10:04:55 UTC (133 KB) [v4] Tue, 15 Sep 2026 10:20:33 UTC (118 KB)
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