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===== Probabilities for Different Stern Gerlach Analyzers: Instructor's Guide =====

==== Main Ideas ====
  * The fourth postulate of quantum mechanics
  * Probabilities
  * Stern-Gerlach devices
  * Quantization of intrinsic angular momentum

==== Students' Task ====
//Estimated Time: 15 minutes//

Small groups of students must experimentally find the probability that a particle in an initial state will be measured as another state.  That is, they must experimentally find

$$P_{out} \; = \; \vert\langle out \vert in \rangle\vert^{2}$$

where the $\vert in \rangle$ or $\vert out \rangle$ states can be $\vert + \rangle$, $\vert - \rangle$, $\vert + \rangle_{x}$, $\vert - \rangle_{x}$, $\vert + \rangle_{y}$, or $\vert - \rangle_{y}$.

==== Prerequisite Knowledge ====
  * Background knowledge on how the Stern-Gerlach device physically separates particles.
  * The first four postulates of quantum mechanics.
 

==== Props/Equipment ====

  * Computers with the [[props:start#Spins OSP Software|Spins OSP software]]
  * A handout for each student

==== Activity: Introduction ====
First, have the entire class as a whole choose the two Stern-Gerlach devices to both have z-orientation.  Have them connect the $\vert + \rangle$ port to the second z-oriented analyzer, and ask them what happens.  Students should find that if a $\vert + \rangle$ state particle is passed through a second z-oriented analyzer, it will still come out in the $\vert + \rangle$ state.  Provide students with the handout for the activity and have them measure the probabilities for all combinations of x,y, and z analyzers experimentally. Emphasize to the students that the probability they are calculating is \textit{only} the probability of a particle leaving the first analyzer hitting detector out of the second analyzer, not the probability that a particle leaving the oven hits the detector.  Also make sure they fill out the worksheet with probabilities, not the mathematical expressions for the probabilities.

==== Activity: Student Conversations ====


==== Activity: Wrap-up ====
Field any questions students have about the results from the probabilities.  Were any of the results unexpected for them?




==== Extensions ====

This activity is the second part of [[courses:activities:spact:spspin1|SPINS Lab 1]].  It is designed to follow [[courses:activities:spact:sphalfprob|Probabilities in the z-direction for a Spin-$\frac{1}{2}$ System]] and precede the  [[courses:activities:spact:spfairdice|Dice Rolling Lab]].

The full lab is designed to be completed in a two hour lab block, while these individual activities are designed to be integrated into a normal lecture.  We prefer to use the integrated activities, rather than the lab, but both are effective methods.