I Use of an Essentially Ubiquitous Equation

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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
 
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renormalize said:
Look at the Schrodinger-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
 
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