Spin & measurement
Before you start
Why does an atomic beam produce two detector outcomes in a suitable magnetic field? Spin is intrinsic quantum angular momentum, not a hidden ball literally rotating. Begin with the outcomes an experiment can reveal.
The setupAn idealized beam of spin-½ neutral atoms passes through an inhomogeneous magnetic field. Its output channels represent +ℏ/2 and −ℏ/2 measured along the selected direction. Spheres only mark atom positions.
What to do and noticeAn unpolarized beam gives both outcomes. Prepare +z, then measure z again. · Turn the analyzer to 90°: individual results are random, but many trials approach equal proportions. · Insert the middle filter, then measure z again; observe how measurement changes later probabilities.
Predict firstWill results fill every position between the channels?
Understand spin, measurement axes and state preparation through two observable outcomes.
Prerequisites: No prior quantum mechanics is needed. The measurement direction is an axis selected by the apparatus, not the direction the atom travels.Two channels
Predict firstWill results fill every position between the channels?
For an ideal spin-½ system, any chosen axis has two measurement outcomes. An unpolarized beam has no preferred direction; over many trials each outcome occurs about half the time.
How to observe
- An unpolarized beam gives both outcomes. Prepare +z, then measure z again.
- Turn the analyzer to 90°: individual results are random, but many trials approach equal proportions.
- Insert the middle filter, then measure z again; observe how measurement changes later probabilities.
Model notes
This samples quantum predictions for ideal spin-½ measurements using a neutral-atom apparatus schematic, not free electrons in a conventional Stern–Gerlach experiment. Paths, colours and splitting distances are schematic, not a shape of spin or a trajectory reconstruction. Spin states are not simply prewritten up/down labels; ℏ = h/(2π).