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- Thread starter NewGuy
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- #1

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- #2

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I seem to remember of proving something similar. I'll dig up my QM notes and try to clear thing up, unless someone answers by the time I get to my office.

- #3

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If you would that I would be very grateful :)

- #4

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I am sorry, but I will fail you too. What I did is to solve problem 1.3. from Sakurai where it is required to show that determinant of [itex]\pmb{\sigma}\cdot\pmb{n}[/itex] is invariant under operation you quoted. I used 3.2.34, 35, 39 and 44.

Middle result of this solution that may help you is:

[itex]U(\pmb{\sigma}\cdot\vec{a})U^\dagger=\pmb{\sigma}\cdot (\vec{a} cos \phi + 2 \hat{n} (\hat{n} \vec{a}) sin^{2}(\phi /2) - (\hat{n} \times\vec{a}) sin \phi ) [/itex]

Where U is given by 3.2.44. Hope it helps to any amount, I wish you luck with your problem.

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