Answer Happy

Dirac Notation and the Stern-Gerlach Experiment The following inner products represent the set of all Stern-Gerlach (S-G) experiments that can be performed with the kets (+),[+),|+)y. (1) (+) |) ཚེ ཚེ ོ y(+/+) 2 c(+|+ y(+/+), T (+1+), (5) (6) (7) y (++) However, not all of them are unique, and by this I mean the following. For example, using the states (+) and |-), we can have four possible S-G experiments: (+1+), (+/-), 1-1+), and (-1-). However, the experiments (+1+) and (-1-) are not unique in that they both tell you what happens when you project one of the base states onto itself. In the same way, (+1-) and (-1+) are not unique as they tell you what happens when you project a base state (vector) on an orthogonal base state. Thus, out of four possible sets of experiment, there are only two sets of unique ones. And so, you can state that (+1-) and (-I+) are essentially the same experiment and it is then sufficient to carry out the calculation only for one of them. For each of the following Dirac brackets: (a) List out all the possible experiments that these brackets correspond to. (b) Sort the experiments into the sets that are unique, as described above. (c) For one representative from each of the groups of unique experiments, draw the corre- sponding schematic or 'box' diagram as we have been doing in class. (d) Perform the corresponding calculation for the output probability for this experiment using Dirac notation and confirm that the results agree with the experimental facts. You must show intermediate steps as this is good practice to familiarize yourself with symbolic manipulations using Dirac notation.
The unique experiments I counted are listed below. If you see a For F symbol, then the way to read this is to match the top symbols to form one Dirac (braſc|ket) and the bottom symbols to form another one. For example, (+/+) is two inner products, namely: (+1+) and, (-1-). Or, (+1+) is the two inner products (+1+) and (-I+). 1. z-z (2) (a) (+/+) (Same) (b) (F) (Opposite) 2. z-x (2) (a) c(+|+) (Same) (b) x (F) (Opposite) 3. z-y (2) (a) y(+|+) (Same) (b) y(+|+) (Opposite) y T 4. x-y (4) (a) y (+1+) (Same) (b) yk-1-12 (Same) (c) y 1-1+x (Opposite) (d) y(+1-2 (Opposite) y Y