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

 

Exercises for the Spin Eigenstate: |x+>

~~1. Run the |x+> (spin eigenstate) simulation with the first ideal Stern-Gerlach apparatus oriented in the X direction.  Begin with the scenario in which the second analyzer has the same orientation as the first.  Predict, then describe the results of the experiments (predict % of the spin-1/2 particles that will reach each counter). 

 

~~2. Now change (click it) the second analyzer to Y and then Z (keeping the first analyzer oriented in the X direction).  What do you expect will the difference between experiments with the second ideal Stern-Gerlach apparatus oriented in the Y or Z direction as opposed to the X direction?  Run the experiment and note the % of the spin-1/2 particles that reach each counter.

 

~~3. Now change (click it) the first analyzer to Y and then Z and change, and keep, the second analyzer oriented in the X direction.  What do you expect will the difference between the results of these experiments versus the ones with the second ideal Stern-Gerlach apparatus oriented in the Y or Z direction?  Run the experiment and note the % of the spin-1/2 particles that reach each counter.

 

~~4. Explicitly compare the results when the ideal Stern-Gerlach analyzers are ordered ZX and XZ, respectively.  Is there any difference in the % of counts at each detector?  Are the final states, upon going through the second analyzer, the same?