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An Interactive Monograph · Edition i

Quantum

A book you can turn the knobs on.

Fifteen phases · 57 chapters · from a glowing oven that should have radiated infinite energy to the open questions that the Standard Model still cannot answer. Read the prose, then drag the slider until the equation does what the words promised.

Volume i & ii

Hydrogenic Atoms to Particles & Fields

Volume i (phases 01–09) builds quantum mechanics from the rubble of 1900 to a working model of atoms and molecules. Volume ii (phases 10–15) opens with the particle zoo and ends at the leap to quantum field theory.

  1. § i · Phase 01

    The Quantum Crisis

    Classical physics had a cabinet of nagging mysteries by 1900 — a glowing oven that should have radiated infinite energy, a metal that emitted electrons only above a colour threshold, and a hydrogen lamp whose spectrum was a barcode rather than a smear. This phase walks the four blows that broke the classical worldview.

    1. 01.01 Planck's catastrophe Why a glowing oven cannot radiate the ultraviolet 8 min
    2. 01.02 Einstein's photons Light arrives in quanta of energy hν 7 min
    3. 01.03 Balmer's ladder Hydrogen's spectrum is a barcode, not a smear 6 min
    4. 01.04 Bohr's leap Quantised orbits patch the Rutherford atom 9 min

  2. § ii · Phase 02

    Matter Waves

    If light could be granular, perhaps matter could be wavy. De Broglie's wavelength turned electrons into standing waves, Schrödinger wrote the equation that governs them, Born told us what they mean, and Heisenberg showed what the wavefunction forbids.

    1. 02.01 de Broglie's wavelength Every particle carries a wavelength λ = h/p —
    2. 02.02 Schrödinger's winter The wave equation that governs all of chemistry —
    3. 02.03 The Born rule The wavefunction is an amplitude for finding, not for being —
    4. 02.04 Heisenberg's uncertainty Position and momentum cannot both be sharp —

  3. § iii · Phase 03

    The Hydrogen Atom

    Solve the simplest atom and the rest of chemistry follows. Spherical symmetry hands us angular momentum on a platter; the radial equation closes with three quantum numbers; and the periodic table emerges as a counting argument rather than an empirical accident.

    1. 03.01 Spherical harmonics The shapes that survive on a sphere —
    2. 03.02 Radial wavefunctions Laguerre polynomials and the nodes of an atom —
    3. 03.03 Quantum numbers emerge (n, ℓ, m) fall out of three boundary conditions —
    4. 03.04 Reading orbitals s, p, d, f and the language of chemists —
    5. 03.05 The periodic table from first principles Why the rows have lengths 2, 8, 8, 18, 18, 32, 32 —

  4. § iv · Phase 04

    Spin

    A magnet split a silver beam in two and nothing classical could explain it. Spin is the irreducible two-state degree of freedom — the qubit before there were qubits — and Pauli wrote the algebra that makes it tick.

    1. 04.01 Stern–Gerlach A magnet splits a silver beam, and reveals spin —
    2. 04.02 Pauli matrices Three 2×2 matrices that generate every spin rotation —
    3. 04.03 The Bloch sphere Every pure qubit state is a point on a sphere —

  5. § v · Phase 05

    Superposition & Time

    A wavefunction is a vector in Hilbert space; time evolution is a rotation in that space. Superpositions beat at frequencies set by energy differences — that is what makes a quantum clock tick, and what makes measurement collapse so jarring.

    1. 05.01 The superposition builder Stack eigenstates with complex coefficients —
    2. 05.02 Time evolution Each eigenstate rotates with phase e^(−iEt/ℏ) —
    3. 05.03 Quantum beats Energy differences are clock frequencies —
    4. 05.04 Measurement and collapse The Born rule applied, the wavefunction reduced —

  6. § vi · Phase 06

    Tunneling

    A particle can pass through a wall it does not have the energy to climb. That single fact powers nuclear fusion in the Sun, the alpha decay of heavy nuclei, and the scanning microscope that imaged the first atom.

    1. 06.01 Through the barrier Exponential decay inside, finite amplitude beyond —
    2. 06.02 Alpha decay Gamow's tunneling clock for unstable nuclei —
    3. 06.03 Scanning tunneling microscopy Atoms imaged one at a time, with a tunneling current —

  7. § vii · Phase 07

    Wavepacket Dynamics

    A free electron's wavepacket spreads; a confined one breathes; one sent through two slits builds its interference pattern one click at a time. Time-dependent quantum mechanics, in pictures.

    1. 07.01 The free particle A Gaussian packet spreads under H = p²/2m —
    2. 07.02 The double slit, revisited One electron at a time, an interference pattern emerges —
    3. 07.03 The harmonic trap Coherent states slosh without spreading —

  8. § viii · Phase 08

    Molecules

    Two atoms approach. Their atomic orbitals overlap, splitting into bonding and antibonding combinations. From this single principle — linear combinations of atomic orbitals — the entire grammar of covalent chemistry unfolds.

    1. 08.01 LCAO bonding Linear combinations split into bonding and antibonding —
    2. 08.02 sp hybrids Methane's tetrahedron is geometry, not luck —
    3. 08.03 The H₂ bond length Where the energy curve has its minimum —
    4. 08.04 Towards benzene Six π electrons in a ring, aromatic stability —

  9. § ix · Phase 09

    Pauli & the Periodic Table

    Electrons are fermions; no two share the same state. That bare statement is why matter has volume, why metals conduct, why the periodic table closes at rows of 2, 8, 8, 18, 18 — and why noble gases are noble.

    1. 09.01 Pauli exclusion, revisited Antisymmetric wavefunctions and the Slater determinant —
    2. 09.02 Hartree–Fock Mean-field many-electron atoms, solved self-consistently —
    3. 09.03 Why noble gases are noble Closed shells and the chemistry of nothing —

  10. § x · Phase 10

    The Particle Zoo

    Volume II opens. The atom is no longer the smallest interesting object; the protons inside it have constituents, and around them swirl a menagerie that the cosmic rays threw at physicists for thirty years before the Standard Model put them in a table.

    1. 10.01 The discovery sequence From electron (1897) to Higgs (2012), in order —
    2. 10.02 The Standard Model table Six quarks, six leptons, four force carriers, one Higgs —
    3. 10.03 Three generations Why nature copied the electron family three times —

  11. § xi · Phase 11

    Mass & Scale

    Why is the electron 1836 times lighter than the proton? Why are neutrinos almost massless? Mass is not a free knob — it ties to coupling to the Higgs field, to binding energy, and to scales that span 30 orders of magnitude.

    1. 11.01 The mass ladder From neutrino to top quark, log-scale —
    2. 11.02 E = mc² Mass is locked-up energy, and the proton proves it —
    3. 11.03 Why neutrinos are light The seesaw, in pictures —

  12. § xii · Phase 12

    Quarks & Hadrons

    Quarks come in three colours and never appear alone. The strong force binds them into mesons and baryons, and the proton — the workhorse of all chemistry — turns out to be a roiling sea of quarks, antiquarks, and gluons.

    1. 12.01 Colour confinement Why a free quark has never been seen —
    2. 12.02 Mesons and baryons Two-quark and three-quark bound states —
    3. 12.03 The proton, up close A sea of partons, not just uud —

  13. § xiii · Phase 13

    Feynman Diagrams

    Squiggly lines that look like cartoons are, when read carefully, the most successful predictive instrument physics has ever produced. Vertices encode interactions; propagators encode travel; loops encode quantum corrections.

    1. 13.01 Vertices and propagators The grammar of QED diagrams —
    2. 13.02 Electron–electron scattering Møller scattering at tree level —
    3. 13.03 The beta-decay diagram A neutron, a W boson, an electron, an antineutrino —

  14. § xiv · Phase 14

    Fields as Particles

    A particle is a quantum of a field; a field is a particle's home everywhere at once. The Fourier modes of a free field are harmonic oscillators, and quantising each one delivers the entire particle content of the theory.

    1. 14.01 Fourier modes as quanta Each mode is a harmonic oscillator —
    2. 14.02 Vacuum fluctuations The Casimir plates feel them —
    3. 14.03 The leap to QFT From single-particle Schrödinger to many-particle fields —

  15. § xv · Phase 15

    Stellar Quanta

    Cosmic objects hide the most extreme quantum experiments. The sun's core fuses hydrogen by tunneling through Coulomb walls. White dwarfs and neutron stars are held up by Pauli exclusion alone. Black holes evaporate slowly because the vacuum is not empty. And spacetime itself rings when two of them collide.

    1. 15.01 Stellar fusion Tunneling through Coulomb walls powers the sun 12 min
    2. 15.02 White dwarfs When Pauli holds back gravity 11 min
    3. 15.03 Neutron stars A star with the mass of the sun, the size of Manhattan 12 min
    4. 15.04 Core-collapse supernovae The neutrino burst that lights a galaxy 13 min
    5. 15.05 Hawking radiation Even a black hole evaporates 13 min
    6. 15.06 Gravitational waves Listening to spacetime ring 12 min

  16. § xvi · Phase 16

    Open Questions

    The Standard Model is the most predictive theory in human history and we know it is incomplete. The book ends where physics is honestly stuck — on what holds galaxies together, on why the Higgs is so light, and on how to put gravity in the same language as the rest.

    1. 16.01 Dark matter The five sixths of matter we cannot see —
    2. 16.02 The hierarchy problem Why is the Higgs not as heavy as the Planck scale? —
    3. 16.03 Quantum gravity The one piece that refuses to fit the puzzle —

¶ Hands-on

Demos & Sandboxes

Standalone interactive widgets. Each one stands on its own — you can land here from a chapter, or wander in from the menu and leave with a feel for the equation you came to see.