A silver atom is prepared with definite spin along
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · Symmetry, angular momentum and spin
The Structure of Quantum Mechanics, Ch The postulates, measurement and collapse
Problem
A silver atom is prepared with definite spin along x, in the state ∣ψ⟩=21(∣↑⟩+∣↓⟩), written in the Sz eigenbasis. It is then sent through a Stern-Gerlach magnet oriented along z, which splits the beam into two components with measured fractions 1/2 and 1/2.Someone argues: 'The atom had a perfectly definite spin state before it entered the z-magnet. The magnet's inhomogeneous field exerts a force on the magnetic moment that disturbs the atom's internal state in an uncontrollable way; that disturbance, not anything fundamental about quantum states, is why we see a 50/50 split. If we could build a gentler magnet that disturbed the atom less, the split would move away from 50/50 and eventually vanish.'
((a)) Say which postulate actually fixes the 1/2,1/2 split, and compute it explicitly from ∣ψ⟩.
((b)) Explain what is wrong with the claim that a gentler magnet would change the split.