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A Spin 1/2 Particle.

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A spin 1/2 particle is in the state |Psi> = Sqrt[2/3] | Up > + Sqrt[1/3] | Down >

Suppose a measurement is made of the spin in the z direction and the result is m_s = -1/2. Now a second measurement is made to determine the spin in the x - direction. What is the probability the spin will be in the +x direction?

So I understand that:
m_s = -1/2 indicates the particle is forced into a downward spin state
Does that mean I should only consider the Sqrt[1/3] | Down > portion of the psi function?
Lastly, I have great difficulty is setting these up. Any suggestion/explanation of working this out would be great.

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