# Finding the Unknown States Leaving the Oven in a Spin-1 System

Keywords: Probabilities, Postulate Four, Quantum Mechanics, Small Groups

### Highlights of the activity

1. Students are placed into small groups and asked to calculate the probability that an unknown state $\vert \psi \rangle$ will be found in the new state $\vert \epsilon \rangle$, where $\epsilon$ can be spin 1, 0, or -1 in the x, y, or z-direction.
2. Using these probabilities, students will find what each unknown state $\vert \psi \rangle$ is in the z-basis.

### Reasons to spend class time on the activity

Students should have previously had experience in Finding Unknown States in a Spin-$\frac{1}{2}$ system. However, the spin-1 system offers a new challenge in the form of a second relative phase term. Finding these unknown states is a good check for students to see if they can effectively utilize the information hidden within the probability values. The instructor can also help formulate a strategy for finding the coefficients in a faster manner than simply looking at every possible probability calculation for the unknown state.

### Student Handouts

Authors: Corinne Manogue

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