A beam of spin- atoms is prepared with a biased coin: each atom
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Density matrices, open systems, entanglement and interpretation
The Structure of Quantum Mechanics, Ch The wave function is not the state
Problem
A beam of spin-21 atoms is prepared with a biased coin: each atom, independently, is put in ∣↑⟩ with probability 43 and in ∣↓⟩ with probability 41. A colleague says the beam is simply in the state ∣χ⟩=23∣↑⟩+∣↓⟩, because a magnet along z gives up three times in four for both. Use ∣+x⟩=21(∣↑⟩+∣↓⟩).
((a)) Check the colleague's claim about the z statistics.
((b)) Compute P(Sx=+ℏ/2) for the beam and for ∣χ⟩.
((c)) Say what is wrong with the colleague's argument.