- #1

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$$S_{avg}=\frac{(S.J)J}{J^2}$$

How to prove this?

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- Thread starter Muthumanimaran
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- #1

- 81

- 2

$$S_{avg}=\frac{(S.J)J}{J^2}$$

How to prove this?

- #2

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- #3

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Im satisfied with the Griffith's explanation for the above expression, but out of curiosity I am looking for the mathematical proof of the same expression. While searching internet about this question, I saw "Wigner Eckart Theorem" could be used to find this expectation value, but I don't know how? Any idea how to do that?

- #4

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I believe that ##\vec S_{avg}## is an operator, not an expectation value. If by "mathematical proof" you mean "Starting with an expression for the time-averaged spin operator, use the Wigner-Eckart theorem to show that $$Im satisfied with the Griffith's explanation for the above expression, but out of curiosity I am looking for the mathematical proof of the same expression. While searching internet about this question, I saw "Wigner Eckart Theorem" could be used to find this expectation value, but I don't know how? Any idea how to do that?

\vec{S}_{avg}=\frac{(\vec S \cdot \vec J)\vec J}{J^2}$$ in the weak field approximation", the answer is "no I don't have an idea how to do that."

However, you don't need the Wigner-Eckart theorem to find the expectation value ##<\vec S_{avg}>.~## Just follow Griffiths, equations 6-73 to 6.75.

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