Calculating Probability of Spin Measurement in System of Particles

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Homework Help Overview

The discussion revolves around calculating the probability of measuring the same spin value for a system of two 1/2 spin particles at time t=0, given a specific quantum state representation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the probabilities associated with the quantum states and question how to determine the likelihood of measuring the same spin values for both particles. There is mention of using conditional probability to approach the problem.

Discussion Status

Some participants have provided insights regarding the probabilities of the states and the conditions under which the spins are equal. There is an ongoing exploration of the implications of these probabilities without a clear consensus on the final calculation.

Contextual Notes

Participants are working within the constraints of quantum mechanics and the specific state representation provided, which may influence their interpretations and calculations.

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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