Question

Answer all of the following questions:

7. (3 pts) Consider the configuration of a particle source (an oven) and 3 analyzers below. Many experimental runs are made with the source producing 400 particles (in thermalized, random states) for each run. The second analyzer is an x-direction spin analyzer, and the first and third are x,y,or z analyzers, but we don't know which kinds (they could both be the same kind). Detector A J 142) Detector B a. On average, what is the maximum and minimum number of particles that can be detected in Detector A? Detector B? Provide and explain an example of a combination of the first two analyzers that would produce, on average, a maximum and minimum each for Detector A and B. Is there more than one combination that can produce these results? Explain. b. For a particular run, Detector A measures a value greater than the maximum you found for part A. How is this possible? c. The particles leaving the middle analyzer are in state [42). If Detector B detects 100 particles on average, what are the possible states (U,)? What combinations of the first two analyzers that could produce this result? d. Provide and explain two examples in which Detectors A and B record the same number of particles on average.

Answer 1

a) The maximum count at the counter can be achieved if both the unknown analyzers are not along x-direction; they can be any one of y or z or both. If N is the initial count of the particles N/2 will reach to x analyzer and then N/4 will reach to the third counter and then N/8 at detector A. This is maximum count. And the minimum count can be achieved if at least one of the two unknown detectors are along the x-direction, then 0 particles will reach the detector A.

So, Maximum count will be N/8 and the minimum count will be 0.

b) This can be possible sometimes because this number is probabilistic. At less number of particles, the experiments can show different result than what probability gives! But if a very large number of particles are studied, then it cannot exceed the probability.

c) The state psi2 will be u/sqroot(2)+ d/sqroot(2) ; where u and d denote the up and down spin states of the particle resp.

We are getting 100 particles at detector B, so the first analyzer is different from the second.

So, the combination of the first two analyzers can be (Y,X) or (Z,X) resp.

d) We must get the equal count in both the detectors A and B for every case. (probability is half for each case)

So, we can arrange the analyzers as follows (any one of the following)

(Y,X,Z); (Y,X,Y); (Z,X,Y); (Z,X,Z)

We will get N/8 count on both the detectors in all the cases mentioned above.