Angular Momentum (Modern Physics)

[roeb]

Homework Statement

This problem is giving me a headache and unfortunately I can't find any example that is similar to it.
A hydrogen atom is in the n = 3, l = 2 state.

(a) What are the possible values of j?

(b) What are the possible values of the magnitude of the total angular momentum including spin?

(c) What are the possible z components of the total angular momentum?

Homework Equations

The Attempt at a Solution

(a)
I believe that j_max = l + 1/2
and j_min = l - 1/2 so...
jmax = 5/2
jmin = 3/2
so
j = 5/2, 3/2

(b)

J = L + S
J = sqrt( j (j+1) )

J1 = sqrt(35)/2 hbar --> (j =5/2)
J2 = sqrt(15)/2 hbar --> (j=3/2)


(c)

j = 3/2; mj = +- 3/2, +- 1/2
j = 5/2; mj = +-5/2, +-3/2, +-1/2


I am very unsure about this whole process. My book unfortunately doesn't have any examples of this process. Can anyone check my work and see if what I am doing is correct? In particular I am very unsure of part b, it just seems a bit strange to me despite following the formula.

Thanks
roeb

 

[borgwal]

it all looks correct!