Preface#
Elementary Computational Physics is a free companion course for anyone learning theoretical physics who actually wants to compute something: to turn the equations on the page into something that runs, plots, animates, and just looks elegant. This course was borne out of my idea to finally have a compendium of exercises – and moderately challenging ones at that! – whose focus was not pen(cil) and paper, but rather the computer.
Each notebook reviews the essential theory, then puts it to work in a sequence of exercises. You implement the physics yourself, visualise it, and finish by validating the result against something independent: a conserved quantity, an analytic limit, a known spectrum, a symmetry. Nothing here asks you to trust a number you cannot check.
The sequence of topics in the course (more or less) follows Wolfgang Nolting’s Theoretical Physics series (Vols. 1–6) — elementary and analytical mechanics, electrodynamics, thermodynamics and special relativity, quantum mechanics, and statistical mechanics. The exercises are written in that spirit and ordering, but the explanations, code, and figures here are original work; this companion does not reproduce the textbooks and is no substitute for them nor for full lectures themselves. Where a full derivation belongs in a book, the notebooks point you there.
The course is now complete, and its shape is worth a sentence. A short set of Meditations opens it — a few pages on what it means to compute in the age of generative AI, and why this course is built the way it is — followed by a Prologue: one gentle notebook that works a single question (how long does a pendulum take to swing?) at three levels of honesty, so you meet the course’s whole method before any formalism. A short Volume 0 — Foundations then precedes the physics: the mathematical and computational tools every later notebook relies on, beginning with floating-point arithmetic and numerical error. Eight physics volumes follow, from projectile motion to the quantum mechanics of many interacting electrons; Volume VII carries a Coda — a three-notebook bridge to many-body formalism (second quantization, Green’s functions, linear response) that the volumes before it never require, and that Volume VIII, the course’s many-body summit — from Hartree–Fock and density-functional theory through real band structures to the Hubbard model, GW, and superconductivity — then speaks as its native language. And the course closes with an Epilogue: four notebooks that gather what no single volume owns — one system seen seven ways, one principle behind every dynamical law, the universality that makes microscopic details wash out at criticality, and, last, an honest account of how a course with no laboratory and no oracle knew its answers were right — followed by a one-page Afterword.
One promise, made here and kept on the last page: every number you compute in this course will be approximate — the very first notebook shows that the computer cannot even represent (1 + ε) − 1 — and the course’s single deepest aim is that you learn to say, and to show, exactly how approximate. The habits that deliver on it appear on every page: results computed more than one way and required to agree; errors separated into their named sources rather than lumped; failures staged deliberately, because knowing the shape of a wrong answer is how you recognise a right one; and a curriculum built to be complete and minimal, where anything borrowed early is derived in full later — every forward reference named, and every one kept.
How to use these notebooks#
Read the theory section first, then work the exercises in order — each builds on the last.
Run everything. The notebooks are meant to be executed and modified; change a parameter and watch what happens.
Don’t skip the validation cells. They are the point: they tell you whether your physics is right.
Use your assistant freely. The course assumes you have an AI assistant and that you use it — the Meditations explain the working arrangement. The few cells you should write entirely by hand are marked; the checks you should never delegate are every one of them.
New to computational work? Start with the Prologue — it is the course in miniature, and it explains the notebook machinery as you go. If you are comfortable already, you may skip straight to Volume 0.
Optional material is marked. Volume VII’s Coda and a handful of capstones are flagged optional; the core course never depends on them.
Animations are pre-rendered so they play anywhere, even on the static website. A few notebooks offer live, interactive versions — launch those on Binder or Colab with the rocket button.
Conventions#
Code style, figure aesthetics, and the validation helpers are shared across every notebook (the ecp
package), so the series reads as one coherent work. The package is small and deliberately readable:
every helper carries a full NumPy-style docstring — help(validate.close) works in any running
notebook — and its complete source is public in the
course’s runnable repository.
Nothing in it is a black box, and reading it is encouraged; it supplies the infrastructure — styling,
validation, animation, the occasional piece of genuine machinery — while the physics, throughout, is
written out on the page. Notebook prose is licensed under CC BY 4.0 and the
code under MIT. Exercise solutions are maintained by the author and are not distributed with the
notebooks; the validation cells are your feedback. To cite the course, use its DOI,
10.5281/zenodo.21418790 (all versions; full metadata in the
repository’s CITATION.cff). The whole course is also available as a single typeset
PDF edition
(2,500+ pages), rebuilt with each release.
A note on how this course was written#
This course was written in collaboration with a generative AI assistant (Anthropic’s Claude), and I say so plainly, because the course’s whole subject is honesty about method. The conception and the curriculum are mine: the arc from a swinging pendulum to superconductivity, the pedagogy that carries it — the rendezvous method, the error budgets, the validation gates, the staged failures — and the detailed per-notebook briefs, worked out number by number, from which every page was built. The assistant drafted prose and code to those specifications, tirelessly and well; I reviewed, corrected, and approved every page, and the final word on every one of them is a human’s. And in the spirit of everything above, neither author was taken on trust: every result in the course is validated against something independent — a conserved quantity, an analytic limit, a known spectrum — precisely so that you never have to take anyone’s word, human or machine, for a single number here.
— Raymond Amador