FewBodyToolkit.jl

A Julia package for solving quantum few-body systems of 2 or 3 particles with general potentials in various dimensions.

Features and modules overview

The FewBodyToolkit.jl package currently provides three modules with the following features:

`GEM2B` - Two-body solver (1D,2D,3D)

Two-body systems in 1D, 2D, or 3D
Symmetric interaction potentials of arbitrary shape
Real- and complex-ranged Gaussian basis functions
Complex scaling method (CSM) for resonances
Basis optimization
Inverse problem: scaling the interaction to yield a desired eigenenergy
Coupled-channel problems with additional derivative terms
Output of the wave function

`GEM3B1D` - Three-body solver (1D)

Three-body systems in 1D
Pair-interactions of arbitrary shape and symmetry (e.g. parity-violating)
Expansion in up to three Fadeev components (rearrangement channels)
Automatic handling of identical particles (symmetrization, reduction of Faddeev components)
Complex scaling method (CSM) for resonances

`ISGL` - Three-body solver (3D)

Three-body systems in 3D
Central-symmetric pair-interactions of arbitrary shape
Expansion in up to three Fadeev components (rearrangement channels)
Automatic handling of identical particles (symmetrization, reduction of Faddeev components)
Complex scaling method (CSM) for resonances
Arbitrary high intrinsic angular momenta (computationally expensive for high values) via infinitesimally-shifted Gaussian basis functions
On-the-fly calculation of central observables and mean-square radii

Installation

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

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

Usage & Examples

All modules follow a similar usage pattern:

1.Casting a few-body system in physical parameters: (reduced) masses, interactions, parity, etc. :

# 2-body system in 3D, with reduced mass mur and potential as interaction
using FewBodyToolkit
potential(r) = -10/(1+r)
phys_params = make_phys_params2B(;mur=2.0,vint_arr=[potential],dim=3)

2.Setting up numerical parameters: number and range of Gaussian basis functions, complex-rotation angle, etc. :

# 10 basis functions with minimum and maximum range parameters 0.5, and 30.0, respectively.
num_params = make_num_params2B(;gem_params=(nmax=10,r1=0.5,rnmax=30.0))

3.Solving the system using the solver provided by the corresponding module.

energies, vectors = GEM2B_solve(phys_params, num_params; wf_bool=1)

4.Post-processing via Plots, optional calculation of wave-functions or mean value of observables.

using Plots
rgrid = range(0.0,5.0,length=100)
firstexcited = GEM2B.wavefun_arr(rgrid,phys_params,num_params,vectors[:,2])
plot(rgrid,firstexcited)

Explicit examples showing this procedure for each of the modules can be found under the Examples page with fully runnable scripts in the /examples subfolder of the repository.

Method and advanced options

More information on the underlying method and basis functions can be found under Gaussian Basis Functions. An explanation of advanced options are listed in Advanced options.

API Reference

See the API section for a list of all exported types and functions.

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