Time-dependent Spin Vector

Highlights of the activity

1. Students calculate $\langle Sx\rangle$, $\langle Sy\rangle$, and $\langle Sz \rangle$ for a general time-dependent state
2. Each group does one calculation to make this time-efficient
3. The results are put together to form the general spin vector $\langle S(t)\rangle$
4. Students then consider what this looks like graphically
5. Students then consider what this looks like when starting in specific states (for example, an eigenstate of Sz)

Reasons to spend class time on the activity

The spin precession calculation is a challenge for students, and if it is done 'for' them they tend to just get bug-eyed and stare. This gives them practice in a practical way (by splitting up the work) with calculating time-dependent expectation values. Then when they see the intimidating $\langle S(t) \rangle$ equation they aren't so daunted by it because they each found a piece of it in their groups. Once this equation is written down, meaning can be made of spin precession. Students can then also look at special cases where we input specific values of theta and phi (corresponding to specific initial states). This special-case practice is not only valuable for their general physics skills but helps them make sense of the equation for $\langle S(t)\rangle $.

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version

spspinvectorguide.pdf