How to write this state vector in coordinate basis?

[Adoniram]

Homework Statement

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:

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,

Homework Equations

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

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.

 

[vela]

Hint: spherical harmonics.