These essays are for someone who met calculus, vectors and a first physics course some years ago and would like to understand quantum mechanics properly now: not as a list of strange facts, but as a theory whose predictions can be followed and checked. No previous quantum mechanics is assumed.

Each essay starts from one concrete question, such as why a hot poker never glows violet or why a beam of atoms splits in two, and ends by answering it. Along the way it restores the mathematics it needs in a few short reminders, works one example with real numbers, and closes with two questions whose answers are worked out, including the easy wrong turns. Longer derivations sit in fold-out sections: open them for the full argument, or skip them; nothing later depends on them.

Start with the first essay and read in order; later essays use what earlier ones set up. The reading order below differs from the file numbering in a few places, deliberately.

The core sequence

1. Why hot objects forced physics to changeWhy does a hot poker glow red, then white, but never violet?
2. Light arrives in individual eventsWhy does dim blue light free electrons from a metal when bright red light cannot?
3. The atom that almost workedWhy does hydrogen emit only certain colours?

4. How alternatives interfereIf an electron is a particle, why are there fringes?
5. One state, different ways to describe itIs a state the same thing as the numbers that describe it?
6. What a wavefunction tells usWhat does ψ at a point mean, and what equation moves it?
7. A practical language for quantum statesWhere do the possible results of a measurement come from, and what sets their chances?
8. Why localisation has a costWhy doesn't the electron fall into the nucleus?

9. Confinement and tunnellingHow does an alpha particle leave a nucleus it lacks the energy to leave?
10. The harmonic oscillatorWhy can't a molecule's vibration be removed completely?
11. Angular momentumWhy can a molecule only rotate at certain rates?
12. Hydrogen without little planetary orbitsWhy the same spectrum as Bohr's, with no orbits?
13. Spin: a two-state quantum systemWhy does a beam of silver atoms split into exactly two?
14. Why identical particles change matterWhy don't all electrons sit in the lowest orbit?
15. How to calculate when exact solutions run outHow close can we get to helium's 79.0 eV, and when can we trust the answer?
16. What measurement predicts, and what it leaves openWhat does the equation say when a detector clicks?

Outside the core sequence, for readers who want to go on. The gravity essay is a side trip; the Dirac essay needs only the two before it.

17. Events, clocks, and spacetimeHow do muons survive a journey more than twenty lifetimes long?
18. Energy, momentum, and massWhy is a helium nucleus lighter than its parts?
19. Gravity as geometry: a short excursionWhy do GPS clocks need adjusting before launch?
20. Toward relativistic quantum mechanicsWhat equation predicted antimatter, and why?

The companion book, Quantum Information, Explained, continues from the core essays: qubits, measurement, entanglement, algorithms, noise and error correction. It assumes the core of this book and none of the optional essays.

The books behind the further reading

Each essay ends with a short list of places to read more, checked against these editions. The essays themselves are written to stand on their own.