Calculating Probability of Spin Measurement in System of Particles

[greisen]

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

 

[Meir Achuz]

The probability of measuring each of the three states is 1/3.
How many of the states have s_1z=s_2z?

 

[greisen]

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

 

[Meir Achuz]

Two states have the same spin,, so the prob is 2/3.