1. The problem statement, all variables and given/known data Basically I need to produce a state for a spin-1/2 particle such that the expectation value of <Jz> = 0 where <Jz> is for a spin-1 particle. 2. Relevant equations Jz = (1 0 0, 0 0 0, 0 0 -1) <--[3x3] matrix 3. The attempt at a solution I don't quite understand how to do this because up till now we have been trying to find expectation values for observables in same spin states. Anyways heres my attempt: ψ* Jz ψ = <Jz> = ψ* (1 0 0, 0 0 0, 0 0 -1) ψ the reason I get no further than this is cuz I don't see how i'm supposed to find a spin-1/2 state which would be in the form of a [2x1] matrix and then multiply the [3x3] matrix by a [2x1] matrix, whats the deal here? I'm guessing i've completely misinterpreted something but I can't see what. .