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

 

Which Way Exercises

These examples depict the measurement of a beam of spin-1/2 particles (each green node sends in a different initial state through the analyzers) as they pass through an interferometer.  One can choose the order of the measurement (for example ZX or XZ) and also one can  "watch" or "not watch" the particles go through the analyzers by toggling the purple button.   The blue analyzers can be clicked to change their orientation.

 

~~1. In which simulation (initial state) and orientation of analyzers (click to change) does "watching" not change the result of the experiment?  For each initial state combination and each analyzer combination, note the % of the spin-1/2 particles that reach each counter.  Why? 

 

~~2. In which simulation (initial state) and orientation of analyzers (click to change) does "watching" change the result of the experiment?  For each initial state combination and each analyzer combination, note the % of the spin-1/2 particles that reach each counter.  Why?

 

~~3. What does "watching" and "not watching" do to the wave function describing the spin state of the particles?

 

~~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?  Does "watching" make a difference?  Are the final states, upon going through the second analyzer, the same?