Plate
particles
About the prints
The chamber solves the time-dependent Schrödinger equation live, on a 256 × 128 grid, by the split-step Fourier method: exact for free motion, with the potential applied in two half steps. Units: ħ = m = 1. The wave’s total probability stays 1 except where it leaves through the soft edges of the chamber.
The dots in the chamber are a halftone print of |ψ|², the probability of finding the particle there: bigger dots, more likely. The plate on the right records where particles are actually found. Each particle is the same wave; when it reaches the plate it is found at one place, chosen at random with the probability the wave gives (the Born rule). The sideways scatter of dots across the plate is only for visibility; the plate measures height alone.
Looking inside a small circle is a measurement: the particle is found there with probability equal to the wave’s share inside it. If it is found, the rest of the wave vanishes; if not, the part inside vanishes. Either way, the wave is renormalised and carries on.
Hydrogen orbitals are exact solutions, shown as a slice through the nucleus (a Bohr radius is 0.053 nm). “Look” there samples electron positions from |ψ|² in that slice, so the dots build up the orbital’s shape.
Space pause · F fire one · 1–7 exposures · C crests.
Drawn for clarity: the halftone, the dot scatter on the plate and the slowed-down playback. The chamber is two-dimensional, walls are tall potential steps rather than perfectly hard, and the edges absorb rather than reflect.
Further reading: Feynman Lectures, Volume III, chapter 1 · Griffiths, Introduction to Quantum Mechanics
Theoria · Quantum waves 0.4 · The particle darkroom