dirac-equation

USEL is an open-source CPU-based scientific computing framework for computational physics and quantum research. It provides modular numerical tools, reusable components, and developer-friendly APIs for building scientific applications. Designed for efficiency, portability, and accessibility, it runs on standard hardware without GPU requirements.

The Dirac Engine is a C++ physics engine which simulates quantum phenomena like basic quantum and wave mechanics, spin 1/2 particles and their antimatter partners in 1D, 2D and 3D.

Lean verified Science.

水素原子とヘリウム原子に対するSchrödinger/Scalar Dirac/Dirac方程式のソルバー

Quantum walk hydrodynamics

Klein–Gordon and Dirac limits of dynamical proper-time phase transport: spin holonomy and antimatter as geometric orientations.

A high-performance Python application for visualizing relativistic hydrogen-like wavefunctions and dipole transitions using the Dirac equation.

Open, relativistic off-diagonal ionization form factors F(s, E0) for quantitative STEM-EDX and ALCHEMI, with reproducible generation and executable data contracts, powered by a zero-dependency Julia atomic scattering engine.

Visualizing the kinematics of relativistic wave packets

Paper I — Geometry First

A novel solution to the Klein-Gordon equation in the presence of a strong rotating electric field

Exact symbolic verification ledger for: Fermion quantum field theory on curved and non-inertial backgrounds in standard-Minkowski form

Solve Dirac equation for the electrons in an isolated atom