Angular Momentum: Adding Electron Spin in Hydrogen Atom

[indecicia]

Homework Statement

An electron with spin up is in the state |n=5, l=1, s=0> of the hydrogen atom. If you could measure the angular momentum of the electron alone, what values might you get and what is the probability of each.

Homework Equations

This problem involves adding angular momenta.
l-s,...,|l-s|= ?

The Attempt at a Solution

spin up means the spin is +1/2
The state ket for the electron is |l=1,s=0>|1/2, 1/2>
1+ 1/2= 3/2
1 - 1/2= 1/2
These are the two possible values for the angular momentum of the electron, so it must be something like
|1,0>|1/2,1/2>= ____|3/2,1/2>+ _____|1/2,1/2>
I don't know how to find the coefficients which (squared) would give the probabilities. Laddering? But where do I start?

 

[indecicia]

Actually I have to find the possible angular momenta squared and their probabilities but it amounts to the same thing.

 

[indecicia]

i think i got it.

 

[Marty]

I got to thinking about this topic and came up with some problems of my own, so I started a thread in Quantum Physics under the heading "Change of Basis for Spin States". Just thought I'd point it out in case you're interested.