1
vote
1answer
180 views

Is the spin 1/2 rotation matrix taken to be counterclockwise?

The spin 1/2 rotation matrix around the z-axis I worked out to be $$ e^{i\theta S_z}=\begin{pmatrix} \exp\frac{i\theta}{2}&0\\ 0&\exp\frac{-i\theta}{2}\\ \end{pmatrix} $$ Is this taken to be ...
4
votes
2answers
909 views

Pauli matrix rotations

When doing physics with two-level systems and introducing rotations, a term that appears quite often is the rotation of a pauli matrix by another one: $e^{- i \sigma_i \theta/2} \sigma_k e^{i ...
3
votes
1answer
730 views

What is the spin rotation operator for spin > 1/2?

For spin $\frac{1}{2}$, the spin rotation operator $R_\alpha(\textbf{n})=\exp(-i\frac{\alpha}{2}\vec{\sigma}\cdot\textbf{n})$ has a simple form: ...
2
votes
1answer
725 views

Help understanding a Magnetic Levitation “Physics Toy”

I was shown a toy, yesterday, which I would like help understanding qualitatively. A fellow engineer showed me a kit which included three main parts: 1.) A base (black box), approximately 4 ...