2025-07-24 –, Main Room 6
We present TwoBody.jl, a Julia package for solving quantum mechanical two-body problems in hadron physics, quantum chemistry, and other fields. This package has several methods for solving the Schrödinger equation. Since this package allows users to construct custom Hamiltonians, it is well-suited for general two-body problems. Software testing is performed using Antique.jl. We present the research and the development workflow using these two Julia packages.
One of our targets, the quark model describes the spectra and structures of mesons. These potentials have several terms. For example, the Cornell potential has three terms: a constant term, a linear term, and a Coulomb term. Furthermore, a hyperfine interaction term is added in our case: A. J. Arifi, L. Happ, S. Ohno, M. Oka, Phys. Rev. D 110, 014020 (2024). Therefore, the Hamiltonian should be flexibly customized for exploring models.
The Hamiltonian is defined as a struct and processed with multiple dispatch in Julia. The Schrödinger equation is solved by the Rayleigh-Ritz method with Gaussian basis functions. In the alternative calculations, the neural network was employed as trial wave functions in the variational method. Implementations of these methods will be published as TwoBody.jl. This package provides a comprehensive solution to quantum mechanical two-body problems including quark models of mesons. It can be applied not only to hadron physics but also to quantum chemistry and other fields.
Each method is tested by comparing its numerical solutions with analytical solutions of the hydrogen atom provided by Antique.jl. This package is useful for developing and testing numerical methods for quantum mechanical systems. It is also useful for educational purposes, and we hope that textbooks for quantum mechanics will be written using Antique.jl.
We acknowledge all contributors and sponsors. S. O. was supported by the RIKEN Junior Research Associate Program. A. J. A. and L. H. were supported by the RIKEN Special Postdoctoral Researcher Program. A. T. was partially supported by JSPS KAKENHI Grant Numbers 20K14479, 22K03539, 22H05112, and 22H05111, and MEXT as "Program for Promoting Researches on the Supercomputer Fugaku" (Grant Number JPMXP1020230411, JPMXP1020230409).
Akio Tomiya is a Full-Time Lecturer in the Department of Mathematical Sciences, Major in Information Mathematics, Faculty of Contemporary Liberal Arts at Tokyo Woman’s Christian University. Born in Takarazuka, Hyogo Prefecture in 1987, he received a BSc from the University of Hyogo in 2010, followed by an MSc (2012) and PhD (2015) in Physics from Osaka University. He has served as a Postdoctoral Researcher at Central China Normal University, and an SPDR Postdoctoral Researcher at the RIKEN BNL Research Center. From 2021 to 2024, he was a Tenured Assistant Professor at Osaka International Professional University of Technology in Osaka. His research focuses on lattice gauge theory, machine learning, and quantum computing. He is a recipient of the 29th Physical Society of Japan Paper Award (2024) and the 14th Particle Physics Medal Award for young researcher (2019). Further details are available on his website:
https://www2.yukawa.kyoto-u.ac.jp/~akio.tomiya/aboutme.html.
Shuhei Ohno is a Ph.D. student (D3) at Yokohama City University and a junior research associate (JRA) at RIKEN in Japan. Shuhei developed Antique.jl for software testing in quantum mechanical calculations and for educational purposes in quantum mechanics. TwoBody.jl, a collection of solvers for two-body problems such as diatomic molecules and mesons, is tested using Antique.jl. He will graduate in March 2026 and is seeking a full-time position using JuliaLang. Further details are available on GitHub.
This speaker also appears in:
- Antique.jl: Analytical Solutions of Quantum Mechanical Equations
Special Postdoctoral Researcher (SPDR) at RIKEN (Japan).
Researcher at JAEA