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**1. Homework Statement**

Basically I need to produce a state for a spin-1/2 particle such that the expectation value of <J

_{z}> = 0 where <J

_{z}> is for a spin-1 particle.

**2. Homework Equations**

J

_{z}= (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* J

_{z}ψ = <J

_{z}>

= 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. .

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