1. The problem statement, all variables and given/known data Consider the states with the quantum numbers n = l = 1 and s = 1/2 Let J = L + S What is the dimension of the Hilbert space to describe all states with these quantum numbers? 2. Relevant equations 3. The attempt at a solution I believe the dimension of the Hilbert space is dependent on the number of base vectors. If I am correct, the 'spin-angle functions' would give me the number of bases vector, and thus the dimension of the Hilbert-space. This is dependent on the quantum numbers s and ms, l and ml and j and mj. s=1/2, so ms=-1/2 , +1/2 l=1, so ml = -1, 0, +1 j= 1/2 or 3/2, so mj = -1/2 , 1/2 OR -3/2, -1/2, +1/2, +3/2 For j=1/2 you get 2*3*2=12 different combinations, and for j=3/2 it's 2*3*4=24 different combinations. This gives 36 different base vectors, and therefore the dimension of Hilbert space would be 36? I have no idea how to go from here. I have the book "introduction to quantum mechanics" by D.J. Griffiths. If someone could help me out, it would be greatly appreciated.