A sequential Stern–Gerlach teaching beamline separates two spin outcomes at analyzer A and then measures each branch at analyzer B. Both first outcomes are retained in the counters.
• A prepared spin-½ beam, analyzer A magnet, separated outcome branches, analyzer B magnets and four joint-outcome counters. • Controls for prepared spin direction (°), analyzer A angle (°), analyzer B angle (°) and independent atoms per second. • Four tabs: Quantum bench, Probabilities & measurements, Experiments (with built-in model checks), and Learn & assess.
P(A+) = cos²[(θ−α)/2]; P(B=A | A) = cos²[(α−β)/2] = q; P(B+) = P(A+)q + [1−P(A+)](1−q). A same-axis repeat gives q = 1, even when the initial A outcomes are random.
The model uses ideal spin-½ projective measurements in one plane. The magnetic hardware is representative and the beam deflection is schematic, with no Lorentz-force trajectory solver. Both A branches are retained, and each new atom is freshly prepared.
No. After ideal projection, measuring in the same basis reproduces that outcome.
No. Both branches contribute to this lab’s B statistics.
With an orthogonal second analyzer, agreement and the B-positive fraction approach 50%; with the same analyzer, A is random but every B result repeats its A result.
It uses ideal spin-½ projective measurements in one plane; the magnetic hardware and beam deflection are schematic, with no Lorentz-force trajectory solver.