Experiment 5
In this experiment the electrons coming out of the Electron Gun are in a single (but as yet unknown) quantum state. We will call this state Unknown State 1. Our goal is to analyze that state in terms of spin along each of the three
coordinate axes. For example, the electrons may be in a state given by
ψ = aχ+(x) + bχ-(x)
where
χ+(x) is the state of an electron with spin “up” (with respect to the x-axis) and χ-(x) is the state
of an electron with spin “down” (with respect to the x-axis). We will let a and b be real numbers,
although in general they can be complex. In this case the probability for the electron to be measured
with spin “up” would be a2 and the probability for it to be measured with spin “down” would be
b2.
- What restrictions exist on the values of a and b?
- Double-click on the green arrow next to Experiment 5 in the navigation menu on the left to conduct the experiment. Determine the values of a and
b for this state (there are four possible sets of values, but you need only find one set).
- Now repeat the experiment, again with the analyzer set
to measure spin along the y-axis. Determine the values of a and b for which the initial state can be
represented as ψ = aχ+(y) + bχ-(y).
- Do the experiment again, this time measuring spin along the z-axis. Again, find the values of a and b
such that the initial state is represented as ψ = aχ+(z) + bχ-(z).
- What do these results tell you about the relationship between spin states measured along different
coordinate axes? For example, how is the state χ+(z) related to the states χ+(x) and χ-(x)? If an
electron has a well-defined spin (either “up” or “down”) with respect to one axis, can it also have a
well-defined spin with respect to the other axes?
- Do your results for this experiment fit with the results you have seen in Experiments 3 and 4?