- #1

- 81

- 2

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

How to prove this?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- B
- Thread starter Muthumanimaran
- Start date

- #1

- 81

- 2

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

How to prove this?

- #2

- 11,443

- 4,461

- #3

- 81

- 2

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

- 11,443

- 4,461

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.

Share: