Exercises for
Multiple Measurements of Quantum-mechanical Spin-1/2 Systems

 

Three Analyzer Mixture Exercises

~~1. Run the Mixture simulation.  Predict, then describe the result of the initial orientation of the ideal Stern-Gerlach apparatus experiments.   Note your predictions and results in terms of the % of the spin-1/2 particles that will reach each counter.

 

~~2. Now change the second analyzer (click it) to X and note the results of the experiments (note the % of the spin-1/2 particles that reach each counter).  Change the second analyzer to Y and again note the results of the experiments.  Compare with the scenario when the second analyzer was oriented in the X direction.

 

~~3. Now set up and analyzer the following orientations of ideal Stern-Gerlach analyzers: ZZX, ZXZ, and XZZ.  How do these three orientations (not the results of the experiments) differ?  Is there any difference in the % of counts at each detector when you run the experiments?  Are the final states, upon going through the third analyzer, the same? Explain using the relationship between eigenstates of the different operators.

 

~~4. Now set up and analyzer the following orientations of ideal Stern-Gerlach analyzers: ZXX, XZX, and XXZ.  How do these three orientations (not the results of the experiments) differ?  Is there any difference in the % of counts at each detector when you run the experiments?  Are the final states, upon going through the third analyzer, the same? Explain using the relationship between eigenstates of the different operators.