Application of wavelets to singular integral scattering equations

Abstract

The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms is demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems.

11 pages, 4 figures

References in corpus (4)

• Relativistic calculation of the triton binding energy and its implications
• Two-Body T-Matrices without Angular Momentum Decomposition: Energy and Momentum Dependencies
• Lorentz Boosted NN Potential for Few-Body Systems: Application to the three-nucleon bound state
• Scattering Calculations with Wavelets

Cited by in corpus (5)

• Multiresolution decomposition of quantum field theories using wavelet bases
• Weighted-residual methods for the solution of two-particle Lippmann-Schwinger equation without partial-wave decomposition
• Wavelet Methods in the Relativistic Three-Body Problem
• Direct numerical solution of the two-particle Lippmann-Schwinger equation in coordinate space using the multi-variable Nystrom method
• Numerical study of the two-boson bound-state problem with and without partial-wave decomposition