A mathematical-physics engine written in Rust, callable from Python. Textbook equations — Schrödinger, Dirac, Harper, Schwarzschild, Casimir, Maxwell — solved by compiled code that is checked against closed-form answers rather than trusted.
Documentation · PyPI · crates.io · GitHub
Three worked examples. Each is an executed notebook or article in which every number is compared against a closed form — nothing is asserted without being checked.
Split-step Fourier evolution of a Gaussian packet against the exact closed form, infinite-well eigenvalues, and the unitarity of the Dirac propagator. Includes the Ehrenfest force that a packet feels near an attractive well — and why unitary evolution can never capture it into a bound state.
Berry phase, Chern number and winding number — the quantities that stay integer under deformation. The winding of $e^{in\theta}$ comes back as an exact integer, which is what makes the Aharonov–Bohm phase robust to disorder and the quantum Hall plateaux flat.
Six equations connecting quantum mechanics to quantum gravity, each solved with pysic-rs and graded against a closed form. Ends with the four solver bugs this exercise exposed in our own library — and why their tests let them through.
New to the library? Start with the getting-started guide, then the special-functions reference, which now carries a plot of every function it documents.
Computational physics in Python tends to be a thin wrapper over a fast kernel, with the interesting parts — the loop over modes, the boundary handling, the root-finding — written in interpreted code. That is where the time goes, and it is also where silent errors hide.
Pysic-rs moves that layer into Rust. The gain is twofold: the loop runs at compiled speed, and the type system removes a class of mistakes (unit mix-ups, uninitialised state, out-of-range indices) before the program runs at all.
The logo is Hofstadter’s butterfly — the fractal spectrum of an electron in a magnetic field. It is not decoration: the Harper equation that draws it is one of the equations the library solves.
Split-step Fourier Schrödinger propagation, and a finite-difference Dirac solver checked against the free-particle dispersion \(E^2 = p^2c^2 + m^2c^4\).
Harper equation, Hofstadter butterfly, Chern numbers and Berry phase — the invariants behind the quantum Hall effect.
Schwarzschild metric, Christoffel symbols and geodesic integration.
Maxwell Green’s functions and radiation, plus the Casimir force between parallel plates via Lifshitz theory.
Gamma, Bessel, Legendre, erf, zeta, Airy and Chebyshev — the primitives everything else is built from.
The Casimir force between parallel plates, for instance, is \(F = -\pi^2 \hbar c A / (240\,a^4)\) — a closed form, which means the solver can be graded rather than merely demonstrated.
The Hofstadter butterfly logo visualizes the Harper equation solved by the library. Use-case cards cover Quantum mechanics, Topology, GR, EM & QED, and Special functions — the five core domains of pysic-rs.
From Quantisation to Quantum Gravity — the mathematical formulation of Schrödinger, Dirac, Maxwell/Aharonov–Bohm, the ADM constraints and Wheeler–DeWitt, each reduced to the invariant a correct implementation must preserve. Alongside Mathematical Foundations for the numerical skeleton underneath.
A Validated Mathematical-Physics Engine in Rust, and What Grading It Against Closed Forms Revealed — the library's design, the mathematical formulation of six equations it solves, and a post-mortem of the eight incorrect routines this work exposed in our own code, with an analysis of why their tests could not have failed.
30 pages, 34 exercises with full solutions (in French). Complex analysis and special functions, floating-point cancellation, spectral linear algebra, ODE stability, Fourier and Strang splitting, asymptotics and turning points, Clifford algebra, and constrained systems. The thread running through it is one question: how would I know this result is wrong?
Every solver ships with a test that compares it against a closed-form result or a textbook value. That is the difference between code that should be right and code that is demonstrably right, and it is the reason the library is usable as a reference implementation rather than a starting point.
The same discipline runs through the sibling projects: optimiz-rs for numerical primitives, Polarway for the data layer, and ThotBook-AI for the local-first LLM toolset, which uses physics-informed neural networks to check the equations it reads in papers.
Use cases