Applications of the Pauli matrix identity (σ·A)(σ·B) = A·B + iσ·(A×B)

[topsquark]

TL;DR

I've always seen this equation derived in my QM classes, but I've never actually seen it used.
$( \sigma \cdot \textbf{A} ) ( \sigma \cdot \textbf{B} ) = \textbf{A} \cdot \textbf{B} + i \sigma \cdot ( \textbf{A} \times \textbf{B} )$

I've taken three intro QM classes, and I have four textbooks that cover the derivation of this equation:
$( \sigma \cdot \textbf{A} ) ( \sigma \cdot \textbf{B} ) = \textbf{A} \cdot \textbf{B} + i \sigma \cdot ( \textbf{A} \times \textbf{B} )$

All of them say this equation is very important, but I just realized yesterday that I've never actually seen the thing used.

What is this equation actually used for?

Thanks!

-Dan

 

[renormalize]

What is this equation actually used for?

Look at the Schrödinger-Pauli equation: https://en.wikipedia.org/wiki/Pauli_equation

 

[topsquark]

Look at the Schrödinger-Pauli equation: https://en.wikipedia.org/wiki/Pauli_equation

Ah! Yes, I have run into that before, but I never spent much time with it. I never recognized the form.

Thanks!

-Dan