Question

Expectation value of two spin 1/2 particles where particle 1 along z axis and particle 2 along another axis?

Answer 1

So I got to thinking that Sn2=ℏ2cosθ(100−1)Sn2=ℏ2cos⁡θ(100−1) making the argument that the z-component of particle 2 is projected onto n^n^. It gave the right answer for the expectation value ⟨Sz1Sn^2⟩⟨Sz1Sn^2⟩ but I am thinking it has to be wrong. That a measurement along n^n^must also return the same eigenvalues as Sz1Sz1, namely ±ℏ2±ℏ2 thus Sz1=Sn2Sz1=Sn2. Is this correct

hope it helps you

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¶potter¶

Answer 2

HEY MATE ⭐⭐⭐
HERE'S THE ANSWER ✌
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for a two spin 1/2 particles, the expectation value of ⟨Sz1Sn2⟩⟨Sz1Sn2⟩ is −ℏ24cosθ−ℏ24cos⁡θ when the system is prepared to be in the singlet state |00⟩=12√(|↑⟩|↓⟩−|↓⟩|↑⟩)|00⟩=12(|↑⟩|↓⟩−|↓⟩|↑⟩).

It is given that the matrix Sz1Sz1 returns particle 1's z component. Where

Sz1=ℏ2(100−1)
Sz1=ℏ2(100−1)

Now for particle 2 the matrix Sn2Sn2 gives the component of spin angular momentum along an axis denoted by the unit vector n^n^. where θθ is the angle between the z-axis and n^n^.

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