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Homework Help: Angluar momentum J values.

  1. Jan 7, 2009 #1
    A pair of spin half particles in a bound state. Spin angular momentum operators S1 and S2. In l= 0, no orbital component, the operator for total angular momentum is J = S1+S2

    Possible ang mom states can be denoted by |J, M> where J and M are quantum numbers for J^2 and Jz respectively. Write down the two possible values of J and corresponding eigenvalues of J^2. For each J list allowed M.


    J^2 eigenvalue for a given J is J(J+1)hbar^2. The two possible values of are J=1 eigenvalue 2hbar^2 and J=0 eigenvalue 0

    Sorry long question! Why is J = 1 and J=0. Couldn't it also be J=-1? Or can S1 and S2 only be 1/2 or 0?

  2. jcsd
  3. Jan 7, 2009 #2
    you just said two spin half particles. therefore s1 and s2 are either +1/2 or -1/2
    but we add them using the addition of angular momentum theorem

    classically you just add them and the possibilities are -1,0 or 1

    quantum mechanically j takes values ranging from |s1|+|s2|,.....,||s1|-|s2||

    so if s1,s2 are either 1/2 or -1/2 then |s_i|= 1/2
    and so j ranges from 1 to 0
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