Probabilities for Different Spin-1 Stern Gerlach Analyzers
Highlights of the activity
- Students are placed in small groups and asked to find the probability of measuring an initial state $\vert \psi \rangle$ in the new state $\vert \delta \rangle$, where $\psi$ or $\delta$ can be spin 1, 0, or -1 in the x,y, or z-direction.
- Time permitted, students could also be challenged to find the spin 1,0, and/or -1 states in the x or y-direction in terms of the z-basis using the probabilities measured in this experiment.
Reasons to spend class time on the activity
Before performing this activity, students are typically very familiar with the Spin-$\frac{1}{2}$ system and the expected probabilities for any of the x,y, or z-oriented analyzers. This activity is useful for introducing students to the probabilities of measuring spin states in the x, y, and z-directions. Students will also commonly practice using the fourth postulate of quantum mechanics to compare the theoretical calculations of probabilities to experimental measurements.