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## Homework Statement

I have two separate problems with the same issue; I don't grasp what information the equation of state is giving me.

a. A system with l=1 is in the state [tex]ψ> = (1/√2) 1> - (1/2) 0> + (1/2) -1> [/tex] Find Ly.

b. A spin 1/2 is in the state [tex]ψ> = (1+i)/3 +> + (1/√3) -> [/tex] Calculate <Sz> and <Sx>, find the probabilities of finding [tex]± \hbar/2[/tex] if spin is measured in z direction, and spin up if measured in x direction.

## Homework Equations

## The Attempt at a Solution

I can tell right away that the values are spin quantum numbers, and I assume both are superpositions of states, but I'm not sure what to DO with the given info to turn it into something usable. I have the griffiths textbook, but I'm not getting anything out of it or in my class notes about what the integers here represent, all my info is for vectors, and scouring the internet has so far failed me. If someone could point me to some relevant material/examples, or explain how to translate this(into matrices, I believe?) I'd be very grateful. Thanks!