A beam of spin- silver atoms passes through three Stern-Gerlach magnets in…
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · The formalism of quantum mechanics
The Structure of Quantum Mechanics, Ch The postulates, measurement and collapse
Problem
A beam of spin-21 silver atoms passes through three Stern-Gerlach magnets in sequence.Magnet 1 is aligned along z, and only the Sz=+ℏ/2 ("up") beam is kept. Magnet 2 is aligned along x, and only the Sx=+ℏ/2 beam is kept. Magnet 3 is aligned along z again, and the fractions emerging up and down are recorded.Someone argues as follows: "After magnet 1, every surviving atom has Sz=+ℏ/2 with certainty. Magnet 2 exerts a magnetic force only along the x direction, so it cannot change the z-component of spin at all. Therefore every atom that passes magnet 2 still has Sz=+ℏ/2, and magnet 3 must find 100% up and 0% down."
((a)) Identify the error in this argument, naming the postulate it misapplies.
((b)) Give the correct fractions of atoms emerging up and down from magnet 3, out of the atoms that entered magnet 3.