Calculating Probability of Spin Measurement in System of Particles

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SUMMARY

The discussion focuses on calculating the probability of measuring the same spin state for a system of two 1/2 particles at time t=0, represented by the state vector |PSI(0)> = 1/sqrt(3) (|+>_1|+>_2 + |+>_1|->_2 + |->_1|->_2). The probability of measuring each of the three states is confirmed to be 1/3. The conclusion drawn is that the probability of both particles having the same spin state (s_1z = s_2z) is 2/3, based on the conditional probability approach.

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greisen
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Hey,

I am a little confused with this system 1/2 particles spin at t=0

|PSI(0)> = 1/sqrt(3) (|+>_1|+>_2 + |+>_1|->_2 + |->_1|->_2

the values of S_1z and S_2z are measured at t=0. Then I have to calculate the probability that the same value will be found for the two particles.

Any help apreciated
 
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The probability of measuring each of the three states is 1/3.
How many of the states have s_1z=s_2z?
 
hmmm. I get that the probability for the three states is 1/3
P = |<a|a>|^2 for each of the vectors. So the probability for measuring the same state for two particles can be calculated using conditional probability ?

Thanks for your reply
 
Two states have the same spin,, so the prob is 2/3.
 

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