Lab · The Stern–Gerlach Experiment

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Apparatus cross-section — vertical scale exaggerated

Slide after development — and density profile

Starting configurations

Start from a configuration, then move one parameter at a time and watch what breaks.

Optimiser

It looks for the single parameter that, moved a little, improves the configuration most. It does not know the answer: it gropes forward one step at a time, as one would in the laboratory.

Vacuum

Working pressure

The atoms must cross the apparatus without hitting the residual gas: the mean free path must be far longer than the beam.

Source

Crucible temperature

Melting is not enough (962 °C): what counts is the vapour pressure. But too high and the atoms collide in the hole, so the beam is no longer effusive.

Crucible hole ⌀

Do not confuse two different vacuums: inside the crucible the gas is silver vapour at a few pascal (λ ≈ 1 mm), outside it is the pump's residual gas, ten thousand times thinner (λ ≈ 10 m). The collisions that matter all happen within one hole diameter, because just outside the beam density falls as 1/r².

Collimation

Slit width

Narrow = sharp but weak beam. Wide = intense but blurred: the trace broadens until it swallows the splitting.

Slit separation

Magnet (coaxial)

Inner (edge) radius

The sharp inner pole: the smaller it is, the more the field — and the gradient — crowd around it. In the thesis design it is 4 mm.

Outer (groove) radius

The concave outer pole, concentric with the inner one (same centre, as in the section drawing). The radial gap is the difference of the two radii. In the design it is 26 mm.

Eccentricity (centres offset)

At 0% the two circles are concentric (as in the design drawing). Increasing it shifts the inner circle to one side: there the gap narrows and the field concentrates, as in the classic offset edge-and-groove magnet.

Beam position in the gap

Where the beam runs between the edge (0%) and the groove (100%). Near the edge the gradient is very strong but the room is little: the beam risks hitting the pole. The field goes as 1/r, the gradient as 1/r².

Pole-piece length

Geometry

Drift (magnet → slide)

After the magnet the separation keeps growing, and here no gap constrains it.

Exposure

Duration

Derived quantities

Simplified model: coaxial magnet field (concentric edge and groove, as in the design drawing), 1/r gradient, effusion from a Maxwell distribution, exposure times to order of magnitude. Meant for finding workable configurations.

📱

Rotate your phone to landscape

This interactive experiment is cramped in portrait. Turn your phone to landscape to see it all (even if small). For a better experience, open it on a desktop or a tablet with a large enough screen.

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La Quantistica · Local lab · Ch. 01F. Palma

Simulated laboratory, written in 2026 together with GitHub Copilot: a teaching model, not scientific software.