Numerical study of the two-boson bound-state problem with and withoutpartial-wave decomposition

Numerical study of the two-boson bound-state problem with and withoutpartial-wave decomposition | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Numerical study of the two-boson bound-state problem with and withoutpartial-wave decomposition Wolfgang Schadow This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8643369/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract The validation of numerical methods is a prerequisite for reliable few-bodycalculations, particularly when moving beyond standard partial-wavedecompositions. In this work, we present a precision benchmark for the two-bosonbound-state problem, solving it using two complementary formulations:the standard one-dimensional partial-wave Lippmann--Schwinger equation and atwo-dimensional formulation based directly on vector variables. While thepartial-wave approach is computationally efficient for low-energy boundstates, the vector-variable formulation becomes essential for scattering applicationsat higher energies where the partial-wave expansion converges slowly. Wedemonstrate the high-precision numerical equivalence of both methods usingrank-one separable Yamaguchi potentials and non-separable Malfliet--Tjoninteractions. Furthermore, for the Yamaguchi potential, we derive exactanalytical expressions quantifying the systematic errors introduced by finitemomentum- and coordinate-space cut-offs. These analytical bounds provide arigorous tool for disentangling discretization errors from truncation effectsin few-body codes. The results establish a reliable reference standard forvalidating the vector-variable approaches essential for future three- andfour-body calculations. PAC Codes: 21.45.-v , 03.65.Ge , 02.60.Nm , 03.65.Nk Two-body bound state Lippmann–Schwinger equation Momentum space Vector variables Partial-wave decomposition Yamaguchi potential Malfliet–Tjon potential Numerical benchmarks Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 28 Jan, 2026 Reviewers invited by journal 28 Jan, 2026 Editor assigned by journal 22 Jan, 2026 Submission checks completed at journal 22 Jan, 2026 First submitted to journal 19 Jan, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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