Demos
Every interactive demo in the curriculum, each on a page of its own. Play with one here, then follow it back to the lesson where it lives.
Course P.1 — Theoretical Mechanics
Two travelling waves, one wave equation
Send two waves in opposite directions and test whether one wave equation can hold them both.
In 3 placesDo two waves share one wave equation?
Place two harmonic waves on the ω–k plane: they obey the same wave equation only if they share the ratio ω/k.
In 2 placesStanding waves on a pinned rope
Drag the wavenumber and find the only values that fit a rope pinned at both ends.
In 3 placesFourier synthesis
Build a square wave, a sawtooth or a plucked string from harmonics, and watch the overshoot at a jump refuse to shrink.
In 2 placesWavevector magnitude and speed
Build |k| from its components and see that only its length, not its direction, sets ω.
In 2 placesTwo crossing plane waves
Tilt one plane wave against another: any direction works, but only a matching |k| shares their speed.
In 2 placesFringes from two crossing beams
Cross two plane waves and read the fringe spacing from an intensity that no longer moves.
In 2 placesMomentum vs kinetic energy under a constant force
Push with a constant force and compare what each second adds to momentum and to kinetic energy.
In 2 placesLeast action, or stationary action?
Bend a path between fixed endpoints and watch the action: flat at the true path, and a saddle once T passes half a period.
In 1 placeMass on a spring
Change mass and damping and read ω, f and the amplitude envelope of a spring oscillator.
In 3 placesOne gravity slider, two oscillators
Change g and compare a hanging spring, whose beat never changes, with a pendulum, whose beat does.
In 2 placesMomentum on a circle
Constant speed, turning momentum: compare the momentum vector at two points of a circular path.
In 2 placesOne symmetry, one conserved quantity
Switch potentials under a moving particle and see momentum, angular momentum and energy conserved exactly when their symmetry holds.
In 1 placeConserved, but not the energy
Spin a wire with a bead on it: the Hamiltonian stays constant while the energy climbs, because the motor does work.
In 2 placesA blob of states in phase space
Let the pendulum’s flow shear a disk of initial conditions into filaments: its shape goes, its area stays (Liouville).
In 1 placeCourse P.2 — Radiation & the Old Quantum Theory
Course P.3 — Wave–Particle Duality
Photoelectric stopping voltage
Change the light’s intensity and wavelength and see which one moves the stopping voltage.
In 2 placesde Broglie wavelength vs speed
Speed up an electron and watch its wavelength λ = h/(mv) shrink.
In 3 placesStanding wave on a Bohr orbit
Wrap de Broglie wavelengths around an orbit: only whole numbers close the wave, and those are the allowed orbits.
In 2 placesCourse P.4 — The Schrödinger Equation
Course P.5 — Bound States & 1D Potentials
Course 0.3 — Complex Analysis & Fourier Methods
Course 1.2 — Qubits, Superposition & the Bloch Sphere
Course 1.4 — Entanglement & Composite Systems
Questionnaires
Where the centre of mass ends up
Step through four paths and see that potential energy depends on where you end, not on the effort spent.
In 1 placeA ball on a slope
Tilt the slope and walk up it: split the weight along and into the surface, and see that height, not path, sets ΔU.
In 1 placeAn exponential front and the wave equation
Tune k and ω of a real exponential and see when its moving wall keeps pace with the equation’s own speed.
In 1 place