FewBodyToolkit.jl

FewBodyToolkit.jl is a Julia package for solving quantum few-body systems. Currently it supports

• two-body systems in 1D,2D,3D
• three-body systems in 1D and 3D.

A more detailed list of features can be found in the Documentation.

Feel free to try it out! If you have questions, encounter issues, or want to extend the package, please open an issue or submit a pull request.

Installation

To install FewBodyToolkit.jl you can use Julia's package manager

using Pkg
Pkg.add("FewBodyToolkit") # or ] add FewBodyToolkit

Example usage

using FewBodyToolkit

# Define physical parameters: interactions and masses of the particles
v12(r) = -10/(1+r^4)
v23(r) = -8/(1+r^5)
masses = [1.0,1.0,2.0]
pp = make_phys_params3B3D(;masses, interactions=[[v23],[v23],[v12]])

# Define numerical parameters
np = make_num_params3B3D(;gem_params=(nmax=10,r1=0.2,rnmax=20.0,Nmax=10,R1=0.2,RNmax=20.0))

# Solve a 3-body, 3D quantum system with your interaction and masses.
@time energies = ISGL_solve(pp,np) # ~0.5s on an average laptop

Method & Documentation

FewBodyToolkit.jl represents two-body states in the center-of-mass frame using central Gaussian basis functions. For three-body problems, the wavefunction is first split into Faddeev components, then each component is expanded in a product of two Gaussians, one for each Jacobi coordinate.

For full details on the method, basis choices, and research-driven examples, see the Documentation.

Related packages:

• Antique.jl - Analytical solutions to solvable quantum mechanical models
• FewBodyECG.jl - For coulombic few-body systems in 3D, using explicitly correlated Gaussians
• TwoBody.jl - Solutions to two-body systems using various methods, e.g. finite differences
• QMsolve - Solving and visualizing the Schrödinger equation in Python
• MOLSCAT - Atom-molecule scattering in Fortran
• JPublicThreeBodySolver - Solver for Faddeev equations in Java

Citation

If you use FewBodyToolkit.jl in your work, please cite the following:

@misc{happ2025fewbodytoolkit,
  author  = {Happ, Lucas},
  title   = {FewBodyToolkit.jl: a {Julia} package for solving quantum few-body problems},
  year = {2025},
  number = {arXiv:2510.04447},
  eprint = {2510.04447},
  primaryclass = {quant-ph},
  publisher = {arXiv},
  doi = {10.48550/arXiv.2510.04447},
  url = {http://arxiv.org/abs/2510.04447},
  archiveprefix = {arXiv}
}