Two particles with spins S1 and S2 are combined to make a system of spin S, expressed by:
a) Find the product of Ŝ1.Ŝ2 in terms of Ŝ1±, Ŝ2±, Ŝ1z, Ŝ2z.
b) Assume that S1 = 1 and S2 = 2. What is the form of combined state |3, 3 > in terms of eignstates of Ŝ12 and Ŝ22 (or Ŝ1z and Ŝ2z )?
Calculate Ŝz |3, 3 > and Ŝ2|3, 3 >.
Construct |3, 1 > .
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