Tutorial Exercises for
Spin Precession of Quantum-mechanical Spin-1/2 Systems

 

Precession Tutorial Follow Up Questions

In these exercises a beam of spin-1/2 particles (in this case, electrons) leaves an oven incident on an ideal Stern-Gerlach apparatus oriented in the x direction.  The beam is then split into |+> and |−> components and the |+> component is sent through a magnet (red) of and then on to another ideal Stern-Gerlach apparatus before being detected at the counters. 

You may click on a blue SG apparatus to change its orientation.  The magnet's strength can be changed.  The beam of electrons is sent through the magnet for a fixed time equal to t = 2πmec/36|e|.  The number appearing on a magnet, therefore (see the tutorial) represents ωt in degrees.  You can change the strength of a magnet by clicking on the number or by clicking the number and holding down the mouse.

 

~~1. Set up the experiment so that you can test your answers to question 2 of the precession tutorial exercise.  What happens to the original state, |x+>, as the magnetic field increases when the second ideal Stern-Gerlach analyzer is oriented in the x, y and z directions?

 

~~2. If the first ideal Stern-Gerlach analyzer was oriented in the z direction, what happens to the original state, |z+>, as the magnetic field (still oriented in the z direction) increases when the second ideal Stern-Gerlach analyzer is oriented in the x, y and z directions?