Solving Spin Problem: S^2 & Probabilities

[Adamantus]

I'm trying to study for exams and can't get a hold of my professor. Anyway, I'm trying to figure out a problem regarding spin. You're given two particles of different spin and the S^2 is measured. It asks for the possible values you could measure, but wouldn't that just be the eigenvalues defined by S^2|sm>=hbar^2*s(s+1)|sm>? That just seems too easy. (edit: I realized what to do on this part...I was just being stupid. I'm still having trouble with the second part).

And for the second part, you're given the result after measuring the total S(z) and the S(z) of one of the particles. It then asks for what possible values you could get for S^2 and their probabilities. But, and I'm probably misunderstanding the question, isn't the result going to still be s*(s+1), which, considering the spins haven't changed, wouldn't have changed?

 

[dwintz02]

Sounds like you should use the Clebsch-Gordan coefficients for adding angular momenta. But if you want to do it explicitly (as you'd probably have to do on your exam if it was a question) post the two spins you're adding and your work and we can help you along.

It's easier to handle it with known spins than to derive the equation for the coefficients with variables.

 

[Adamantus]

i actually used the clebsch-gordan right before you replied. I am pretty sure that's how ill do it on the exam, since my professor kept repeating throughout the year that we'd have a problem like that on the exam (and have to use the tables). i guess his constant repetition didn't help