Where does the Stern Gerlach term in the Pauli equation come from? Taken from http://en.wikipedia.org/wiki/Pauli_equation. Following wikipedia's steps the Stern Gerlach term pops out when you apply the Pauli vector identity. I don't understand this step. It seems as if there should be no Stern Gerlach term.(adsbygoogle = window.adsbygoogle || []).push({});

Here are my steps starting with the Pauli vector identity,

[itex](\boldsymbol{\sigma} \cdot \boldsymbol{a})(\boldsymbol{\sigma} \cdot \boldsymbol{b}) = \boldsymbol{a} \cdot \boldsymbol{b} + i\boldsymbol{\sigma} \cdot (\boldsymbol{a} \times \boldsymbol{b})[/itex]

[itex](\boldsymbol{\sigma} \cdot (\boldsymbol{p} - e\boldsymbol{A}))^2 = (\boldsymbol{\sigma} \cdot (\boldsymbol{p} - e\boldsymbol{A}))(\boldsymbol{\sigma} \cdot (\boldsymbol{p} - e\boldsymbol{A})) = (\boldsymbol{p} - e\boldsymbol{A})^2 + i\boldsymbol{\sigma} \cdot ((\boldsymbol{p} - e\boldsymbol{A}) \times (\boldsymbol{p} - e\boldsymbol{A}))[/itex]

Shouldn't

[itex]\boldsymbol{v} \times \boldsymbol{v} = \boldsymbol{0}[/itex]

and

[itex](\boldsymbol{\sigma} \cdot (\boldsymbol{p} - e\boldsymbol{A}))^2 = (\boldsymbol{p} - e\boldsymbol{A})^2[/itex]

I did it out in individual components as well, and came to the same conclusion. What am I missing?

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# Stern Gerlach term in the Pauli Equation

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