1999/04/06 by Susanne Bielefeld, S. Bielefeld, J. Ihmels +5
Computer Science · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Quantum Computing Algorithms and Architecture #hep-ph
paper · pdf · doi:10.48550/arxiv.hep-ph/9904241
9 pages, 24 eps-figures, macro svjour included
arxiv created 1999/04/06 · openalex publication_date 1999/04/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By their very nature, field-theoretical Hamiltonians are derived in momentum representation. To solve the corresponding integro-differential equations is more difficult than to solve the simpler differential equations in configuration space (`Schrödinger equation'). For the latter many different and very effective methods have been developed in the past. But rather than to Fourier-transform to configuration space - which is not always easy - the equations are solved here directly in momentum space, by using Gaussian quadratures. Special attention is given to the case where the potential in configuration space is linear and where the corresponding momentum-space kernel has an almost intractable 1/( k - k')4 -singularity. Its regularization requires a certain technical effort, introducing suitable counter terms. The method is numerically reliable and fast, faster than other methods in the literature. It should be useful to and also applicable in other approaches, including phenomenological Schrödinger-type equations.