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.
This problem involves adding angular momenta.
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?