Probabilities in the Z-direction for a Spin-$\frac{1}{2}$ System
Highlights of the activity
- Students are asked to fire a beam of 10, 100, 1000, and 10000 particles into a single z-oriented Stern-Gerlach device multiple times.
- The groups must convince themselves probabilistically and observationally that the probability of a particle being spin-up in the z-direction is $\frac{1}{2}$ and the same for spin-down.
Reasons to spend class time on the activity
Without any context on the SPINS program or the Stern-Gerlach Experiment itself, students have absolutely no reason to believe that a beam of particles would split into two beams after being exposed to a non-uniform magnetic field. This experiment is performed to show students that the SPINS program reflects the true results of a Stern-Gerlach experiment. Students will also perform this experiment to convince themselves probabilistically that the probability of a particle being measured as spin-up or spin-down is $\frac{1}{2}$.