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FewBodyToolkit.jl: a Julia package for solving quantum few-body problems

Lucas Happ

TL;DR

FewBodyToolkit.jl delivers an open-source, Julia-based framework for solving quantum few-body problems by unifying two- and three-body solvers across 1D–3D with arbitrary pairwise interactions. The approach relies on the Gaussian expansion method, leveraging Jacobi coordinates and Faddeev decomposition to build a generalized eigenvalue problem that yields bound and resonant states, complemented by automatic angular-momentum coupling and symmetrization. The work provides a modular, well-documented API with dedicated solvers (GEM2B, GEM3B1D, ISGL), a detailed workflow (validation, size estimation, precomputation, interpolation, and observables), and practical demonstrations through Coulomb, mass-imbalanced, and positronium examples, along with benchmarks. This combination of flexibility, diagnostics, and accessible documentation positions the package as a versatile tool for research, teaching, benchmarking, and method development in quantum few-body physics.

Abstract

Few-body physics explores quantum systems of a small number of particles, bridging the gap between single-particle and many-body regimes. To provide an accessible tool for such studies, we present FewBodyToolkit.jl, a Julia package for quantum few-body simulations. The package supports general two- and three-body systems in various spatial dimensions with arbitrary pair-interactions, and allows to calculate bound and resonant states. The implementation is based on the well-established Gaussian expansion method and we illustrate the package's capabilities through benchmarks and research examples. The package comes with documentation and examples, making it useful for research, teaching, benchmarking, and method development.

FewBodyToolkit.jl: a Julia package for solving quantum few-body problems

TL;DR

FewBodyToolkit.jl delivers an open-source, Julia-based framework for solving quantum few-body problems by unifying two- and three-body solvers across 1D–3D with arbitrary pairwise interactions. The approach relies on the Gaussian expansion method, leveraging Jacobi coordinates and Faddeev decomposition to build a generalized eigenvalue problem that yields bound and resonant states, complemented by automatic angular-momentum coupling and symmetrization. The work provides a modular, well-documented API with dedicated solvers (GEM2B, GEM3B1D, ISGL), a detailed workflow (validation, size estimation, precomputation, interpolation, and observables), and practical demonstrations through Coulomb, mass-imbalanced, and positronium examples, along with benchmarks. This combination of flexibility, diagnostics, and accessible documentation positions the package as a versatile tool for research, teaching, benchmarking, and method development in quantum few-body physics.

Abstract

Few-body physics explores quantum systems of a small number of particles, bridging the gap between single-particle and many-body regimes. To provide an accessible tool for such studies, we present FewBodyToolkit.jl, a Julia package for quantum few-body simulations. The package supports general two- and three-body systems in various spatial dimensions with arbitrary pair-interactions, and allows to calculate bound and resonant states. The implementation is based on the well-established Gaussian expansion method and we illustrate the package's capabilities through benchmarks and research examples. The package comes with documentation and examples, making it useful for research, teaching, benchmarking, and method development.

Paper Structure

This paper contains 30 sections, 13 equations, 3 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Coordinates and Schrödinger equations
  4. Gaussian expansion method
  5. Features
  6. General Features
  7. Module-specific Features
  8. GEM2B: Two-body solver
  9. GEM3B1D, ISGL: Three-body solvers (1D, 3D)
  10. Implementation
  11. Inputs and Outputs
  12. Workflow
  13. 1. Input validation
  14. 2. Size estimation
  15. 3. Preallocation
  16. ...and 15 more sections

Figures (3)

  • Figure 1: Densities of $s$-wave eigenstates of the Coulomb potential. Numerical solutions obtained via https://github.com/lhapp27/FewBodyToolkit.jl are shown as solid lines, exact values provided by Antique.jl as markers.
  • Figure 2: Scaling of runtime (left) and memory usage (right) with basis size $3 n_\mathrm{max}^2$ in a double-logarithmic scale. We compare the total costs when evaluating the interaction matrix elements (i) numerically (blue), and (ii) using analytical expressions (red).
  • Figure :