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Theme 1 — General Introduction and Foundational Experiments

Stern—Gerlach, idée de la quantification

Keywords: Stern--Gerlach · spin · postulat de la mesure · expérience

Exercise 1 : Stern—Gerlach and the idea of quantization

Question 1
A beam of atoms crosses a Stern—Gerlach device along zz; the “spin-up” component is kept. That sub-beam enters a second device, also along zz. What is seen on the screen?

Hint
Think about repeating a projective measurement in the same basis.

Solution
The atoms were already projected onto ∣+z⟩\ket{+_z}; the second filter does not split that component further: a single spot, consistent with the preparation.

Question 2
Same preparation, but the second device is along xx. What happens?

Solution
∣+z⟩\ket{+_z} expands in the xx basis with two nonzero components; two spots appear, each with probability 1/21/2 (barring degenerate magnet alignment).