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

 

Superposition Follow Up Questions

 

~~1. Would an overall phase multiplied to both c+ and c matter to the results of the experiment?  Can such an overall phase, then, be detected?  If you find it hard to answer this question, write out the superposition and simplify the state. 

 

~~2. Did the phase relationship between c+ and c matter to the results of the experiment?  Can such a relative phase, then, be detected? 

 

~~3. Explore these possibilities with the simulation provided in which you may change the initial state going into the X Stern-Gerlach analyzer.

 

In this simulation a beam of spin-1/2 particles leaves an oven incident on an unknown Stern-Gerlach apparatus.  The incident beam is initially a statistical or random mixture of spin-1/2 particles.  To change the initial beam to a superposition of spin states in either the x, y, or z bases click the Edit button: .

You will then see the following dialog:

Choose a basis and then in the row with the Spin 1/2 system reference, enter the real and imaginary coefficients of the spin up (Real 1 and Imag 1) and spin down (Real  2 and Imag 2) components of the initial beam.  You must hit return on your keyboard to have your value entered in the text field.  When you are ready to experiment click the Submit button on the dialog box.