Theme 1

General Introduction and Foundational Experiments

Exercise 1 : Stern—Gerlach and the idea of quantization

Question 1

A beam of atoms crosses a Stern—Gerlach device along

z

; the “spin-up” component is kept. That sub-beam enters a second device, also along

z

. What is seen on the screen?

Hint

Think about repeating a projective measurement in the same basis.

Solution

The atoms were already projected onto

\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

x

. What happens?

Solution

\ket{+_z}

expands in the

x

basis with two nonzero components; two spots appear, each with probability

1/2

(barring degenerate magnet alignment).