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Old Mar 15th 2017, 11:38 PM   #1
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Uncertainty Relation for generic spin-1/2 particle

I'm using the Quantum Systems, Processes, and Information textbook for my quantum mechanics course and working on problem 4.4 below


I feel like there is a shortcut to this answer that I'm missing, because I've done several pages of algebra and simplifications and I can't seem to get a form that either I or Wolfram can simplify into something reasonable.

I'm calculating the uncertainty by using the equation with <A^2> - <A>^2 for some operator A.

I'm using the form of Sx below and corresponding forms of Sy and Sz


And I'm using the definition of expectation value below


However, despite double and triple checking all my algebra, this is the equation I get for the product of the two uncertainties, which is not really workable.

https://www.wolframalpha.com/input/?...cosx*sinx)%5E2))

I feel like I'm certainly missing some major shortcut.

Thanks in advance.

Last edited by Bolshevik; Mar 15th 2017 at 11:42 PM.
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Old Mar 16th 2017, 12:03 PM   #2
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I can't follow what you are doing without the links. Can you try to post it again?

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