Formula for a spin S in a SGE

[Allegra]

A spin S particle goes through two successive Stern-Gerlach experiments, the second one with axe turned by an angle theta.
Is it a formula giving the probability of measuring y in the second device knowing that x has been measured in the first?
To be clear: for spin 1/2, we have the classical formulas:p(1/2|1/2)=cos²(theta/2) and p(-1/2|1/2)=sin²(theta/2).
I've found formulas for S=1.
I'm looking for a generalization for spin S. All I have found is that you have to use Clebsch-Gordan coefficients. Ok, I don't know how to do that. Please what is the formula? I guess it's a classical result.

 

[azntoon]

The formula you are looking for is given by the Wigner-Eckart theorem which states that the probability of measuring a certain value of the angular momentum after two successive Stern-Gerlach experiments is given byP(J2, M2|J1, M1) = |<J2, M2|T|J1, M1>|^2where T is the transition matrix element and <J2, M2| and |J1, M1> are the initial and final angular momentum states. The transition matrix element can be expressed in terms of Clebsch-Gordan coefficients asT = <J2, M2|J1, M1><J1, M1|J2, M2> Since this is a general formula, it is valid for any spin S.