3D Lab
16 modules, 12 3D scenes. Every scene is solved live in your browser — wavefunctions, energy levels, transmission coefficients and Bell correlations are all computed on the spot and recomputed the instant you move a slider. None of it is pre-rendered.
First time here? Start withModule 00: how to use this platform — two minutes.
- 00no sceneCore
How to use this platform
Learn to drive a 3D scene in three minutes, and see why this site insists on "look first, calculate second".
◆ The skeleton every module shares: one-line goal → 3D scene → what to look for → common misconceptions → questions
- 011 ◆Core
Wave–particle duality and the double slit
Watch particles arrive one at a time and pile up into interference fringes that nobody drew in advance.
◆ The first few dozen dots look random; after a few hundred the fringes surface on their own
- 021 ◆Extended
The wavefunction and the Born rule
Turn "ψ is complex and |ψ|² is the probability density" from a slogan into a picture you can rotate.
◆ ψ as a curve writhing in the complex plane, with the real and imaginary parts as its two shadows
- 031 ◆Core
Bound states in one dimension: wells and the oscillator
See where energy levels come from, and why a state that is visibly spinning is called stationary.
◆ The blue ψ tube turns in the complex plane while the purple |ψ|² curtain does not move at all
- 041 ◆Core
Tunnelling and scattering
Watch a wave packet hit a wall it cannot climb, and find part of it on the other side.
◆ The classical ball rebounds along its own path while the packet splits into reflected and transmitted parts
- 052 ◆Core
Spin and the Bloch sphere
Turn a spin state from a pile of complex numbers into a geometric object you can drag, watch precess, and watch collapse.
◆ A sphere on which every point is a pure state; drag it and the |ψ⟩ in the readout follows
- 061 ◆Core
Angular momentum and hydrogen orbitals
Actually see what 1s, 2p and 3d look like, and work out which part of the picture n, l and m each control.
◆ The probability cloud developing dot by dot — each dot a possible outcome of a position measurement
- 072 ◆Extended
Measurement, superposition and collapse
Separate two things that are constantly confused: being in a superposition, and not knowing which one it is.
◆ The same state, a different measurement basis, and a definite outcome turns into fifty-fifty
- 081 ◆Extended
Entanglement and Bell non-locality
Refute, with your own data, the assumption that outcomes were already decided before the measurement.
◆ Each side alone is completely random, yet the two are strictly correlated
- 091 ◆Extended
Time evolution and energy eigenstates
Settle one thing: eigenstates do nothing, superpositions move, and the rate at which they move is the level spacing.
◆ A single eigenstate: the tube turns, the probability density does not budge
- 101 ◆Supplementary
Identical particles and exchange symmetry
See how a purely formal operation — swapping two labels — pushes particles apart or pulls them together.
◆ Swapping two identical particles returns the wavefunction unchanged (bosons) or flipped in sign (fermions)
- 11no sceneSupplementary
The physical picture behind approximation methods
Work out what perturbation theory, the variational method and WKB each actually change, and where each one breaks.
◆ Levels and wavefunctions before and after a perturbation, and how corrections accumulate order by order
- 121 ◆Extended
Open systems and decoherence
Answer one concrete question: why does the macroscopic world look classical?
◆ The Bloch vector shrinking from the surface towards the centre — a pure state becoming mixed
- 131 ◆Supplementary
Getting a feel for the path integral
Build the picture that every path contributes, and watch the classical path emerge from the interference.
◆ Hundreds of ragged paths connecting the same two points, each carrying a phase
- 14no sceneSupplementary
Frontier topics
A set of signposts for going further, and what each direction needs first.
◆ One-line pictures for each direction, and which modules they build on
- 99no sceneSupplementary
Appendix: notation, units and numerical methods
One place for the symbols, units and algorithms used across the site.
◆ The notation and unit conventions used everywhere on this site
Looking for the full derivations and exercises?
The 3D modules build the physical picture; the textbook does the calculation properly. Every module page links directly to the matching chapters, and the sidebar has the whole textbook under "Textbook".