Quiz solution

As pointed out in these solutions, the quiz used the word "probability" in a cavalier manner. Nevertheless, people did pretty well on it and seemed to know what to calculate.

The key starting point was to recognize that, for times after t=0 we need to write the state function as an expansion in energy eigenstates for the t>0 potential system. We can do this because the energy eigenstates form a basis; we want to do this because we know the time dependence of each of these eigenstates. (Also, the coefficients that arise in the expansion are relatively manageable because it is an orthonormal basis.)

In a sense, once we have clearly answered the questions: "what is a mixed state?" and "what is an eigenstate?", we are ready to move on to 3D QM. These are highly nuanced questions and are perhaps related to questions regarding the interpretation and meanings of the state function in quantum physics. We will keep working on it for a while.