Calculating Probability of Spin Measurement in System of Particles

In summary, the conversation is discussing the calculation of the probability of measuring the same spin state for two particles in a system where 1/2 particles are spinning at t=0. The initial state of the system is given, and the values of S_1z and S_2z are measured at t=0. The probability of measuring each of the three states is 1/3, but since two of the states have the same spin, the probability of measuring the same state for two particles is 2/3. The calculation of this probability can be done using conditional probability.
  • #1
greisen
76
0
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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  • #2
The probability of measuring each of the three states is 1/3.
How many of the states have s_1z=s_2z?
 
  • #3
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
 
  • #4
Two states have the same spin,, so the prob is 2/3.
 

1. What is the formula for calculating the probability of spin measurement in a system of particles?

The formula for calculating the probability of spin measurement in a system of particles is P = (m+1)/(2m), where P is the probability, m is the number of possible spin states, and +1 represents the spin state being measured.

2. How do you determine the number of possible spin states in a system of particles?

The number of possible spin states in a system of particles is equal to 2^(n), where n is the number of particles in the system. For example, if there are 3 particles in the system, there will be 2^(3) = 8 possible spin states.

3. Can the probability of spin measurement be greater than 1?

No, the probability of spin measurement cannot be greater than 1. It is a value between 0 and 1, representing the likelihood of a specific spin state being measured in a system of particles.

4. How does the probability of spin measurement change if there are more particles in the system?

The probability of spin measurement increases as the number of particles in the system increases. This is because there are more possible spin states and therefore a higher chance of a specific spin state being measured.

5. Can the probability of spin measurement change over time?

Yes, the probability of spin measurement can change over time. This can occur due to factors such as external influences on the system or interactions between particles within the system. It is important to continuously recalculate the probability as the system evolves.

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