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## 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?