Quantum mechanics simulator

Five interactive views make the core ideas of quantum mechanics visible: superposition on the Bloch sphere, quantised energy in a box, wave-particle duality in the double slit, entangled measurements and quantum tunnelling through a barrier. Each is computed from the governing equations rather than animated by hand.

This interactive simulation runs in your browser with WebGL. Free, no account needed.

What you can explore

Bloch sphere

A single qubit is a point on a glass sphere. Set the polar and azimuthal angles, or apply H, X, Y, Z and S gates and watch the state rotate smoothly across the surface. The sphere glows where a measurement is most likely to land, and the Born-rule probabilities update as you move.

Particle in a box

The wavefunction of a particle trapped between infinite walls, coloured by its complex phase so you can see it evolve in time. Neighbouring lobes always sit on opposite colours, the nodes stay fixed, and an energy ladder shows the levels spaced as n².

Double slit

A wave passes two slits and the two wavelets interfere: bright bands where they reinforce, calm nodal lines where they cancel. Single particle hits land on the detector one at a time and the fringe pattern builds up from random dots. Turn on which-slit measurement and the fringes vanish.

Entanglement

Two particles share a single quantum state. Measure one and the other’s result is fixed instantly, with correlations that no local hidden-variable explanation can reproduce.

Tunnelling

A wave packet meets a barrier higher than its energy and part of it still gets through. Change the barrier height and width to see how the transmission probability falls off exponentially.

Key equations

  • |ψ⟩ = cos(θ/2)|0⟩ + e^{iφ} sin(θ/2)|1⟩
  • ψₙ(x) = √(2/L) sin(nπx/L)
  • Eₙ = n²π²ℏ² / 2mL²
  • d sin θ = mλ

Curriculum

AQA A-level physics, IB Physics HL C.3 and E.1.

Common questions

Why do the fringes disappear when you measure which slit?

Knowing which slit the particle used removes the interference term between the two paths, so the probabilities simply add and the pattern becomes two overlapping single-slit humps.

What does a point on the Bloch sphere represent?

Every pure state of a single qubit. The north and south poles are |0⟩ and |1⟩, and points on the equator are equal superpositions that differ only in phase.

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