Explore waves, spin, entanglement, and the physics of measurement.
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Choose a phenomenon. Every tab has its own model, controls, and physics notebook.Waves → States → Measurements
The double-slit experiment
Preparing the quantum state
One wave function. Two openings. A world of possibilities.ℏ = m = 1
SIMULATION TIME0.00 t
IN THE DOMAIN100.0%
AT THE DETECTOR0.0%
PROBABILITY BUDGET1.000000
FROM POSSIBILITY TO OBSERVATION
A pattern, one click at a time.
0DETECTIONS
The packet is on its way to the screen.
Clicks sample the simulated detector’s absorption. Each cycle represents a Poisson ensemble with 1,200 mean preparations; repeated cycles build statistics.
THE PHYSICS BEHIND THE PICTURE
Amplitudes add. Probabilities interfere.
The two openings create overlapping probability amplitudes. Where their phases align, detection becomes more likely; where they oppose, dark fringes appear.
P = |ψ₁ + ψ₂|²
TRY THIS Increase the slit separation and watch the fringes become more closely spaced.
Lower probability densityHigher
Color strength uses a fixed nonlinear scale to reveal faint waves.
Inside the simulationTHE MODEL · THE MATH · THE LIMITS+
A wave function, evolved.
This is a two-dimensional, nonrelativistic single-particle model. It evolves a normalized Gaussian wave packet under the time-dependent Schrödinger equation in scaled units with ℏ = m = 1.
i ∂ψ/∂t = [−½∇² + V(x,y) − iW(x,y)]ψ
The double-slit wall is a finite potential of height 36. A finite-height wall permits a very small amount of penetration. Slits and barrier widths are represented with cell-averaged potentials, so parameter changes are continuous across grid cells.
A detector with an explicit model.
A smooth complex absorbing potential W ≥ 0 starts at x = 17. Its loss of norm, integrated over x and time, predicts the detected y distribution. Other edge absorbers limit reflections and periodic FFT wraparound.
The budget is surviving probability + detector absorption + other boundary absorption. It should remain close to 1. Detector events are Monte Carlo samples of incremental absorption, with an accelerated Poisson source.
Dots are detector records. The colored field is a probability amplitude visualization; it does not show a definite particle path.
Numerics you can inspect.
A symmetric split-operator Fourier method alternates potential/absorption half steps and a kinetic full step. The 256 × 128 grid covers x ∈ [−24, 24), y ∈ [−15, 15); Δt = 0.025. Speed changes the number of steps per animation update, not Δt.
Finite grid, finite domain, absorber reflection, and time splitting introduce numerical error. Sharp apertures are grid dependent. A near-unity probability budget checks accounting; it does not by itself establish convergence.
Tunneling packets contain an energy spread, including a possible above-barrier tail. This version models coherent dynamics and absorption; it does not include which-path detectors or environmental decoherence.
