Matrix Representation of Spin Operators

Highlights of the activity

1. Students generate matrices that correspond to Sz, Sy and Sx for a spin 1/2 system
2. Students generate spin matrices starting from information about their eigenvalues and eigenvectors
3. Students see that eigenvalues of the spin operators are the values of spin that can be measured for a system, and that the eigenvectors are the states that are possible after a measurement is made
4. Students write down the spin operators as a linear combination of projection operators

Reasons to spend class time on the activity

Students are often confused about the nature of operators in quantum mechanics. In particular, students often believe that the transformation that occurs during a quantum measurement is the same as the transformation caused by the operator of the observable measured. This activity helps students see that an operator that corresponds to an observable encodes information about the results of measurements.

This activity works particularly well when sequenced with other activities:

• Linear Transformations
• Eigenvectors and Eigenvalues
• Projection Operators

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version

Student Handouts

spspinoperatorshand.doc

spspinoperatorshand.pdf

spspinoperatorshand.tex