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How to write this state vector in coordinate basis?

  1. Apr 30, 2015 #1
    1. The problem statement, all variables and given/known data
    I am given this state, which is the result of a lamba particle decaying into a proton and neutral pion. Initial j = 3/2. The final state can theoretically be written as:

    state.jpg

    I have already determined that:
    alpha_p = Sqrt[2/3]
    beta_p = Sqrt[1/3]
    alpha_d = -/+ Sqrt[2/5]
    beta_d = +/- Sqrt[3/5]

    (hopefully that's correct)

    Express the above state vector in the coordinate basis and show that the angular distribution of
    the two final state particles is given by,
    ans.jpg

    2. Relevant equations
    I know that the coordinate basis function will be psi(r) = <r|psi>


    3. The attempt at a solution
    I just have no idea how to calculate <r|psi> on a state vector that only has angular momentum eigenvalues shown (with some coefficients).

    If someone can point me in the right direction, I would really, really appreciate it.
     
  2. jcsd
  3. May 1, 2015 #2

    vela

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    Hint: spherical harmonics.
     
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