Tips for problem set 9

-For Question 1, the textbook questions on Heisenberg Uncertainty (e.g. 24,25,43 in ch40) may be a useful warmup. To do this question, you only need the information given in the question and one uncertainty relation. (There is a way of thinking about this based on single-slit interference, but I would prefer you to answer just using the uncertainty principle). As a start, make sure you understand the answer to the second clicker question on November 21st. If you can explain why the beam spreads out when the hole gets smaller, you should be able to quantitatively say how much it spreads out.

-For Question 2, you may may to look over section 39.7 in the text. Warm-up problems are ch39 #20-24, 30-32.

-Question 3b is much simpler than it seems. The essential point here is that an energy eigenstate remains an energy eigenstate at a later time. Mathematically, we can see this because the energy is related to frequency, and the wavefunctions for energy eigenstates oscillate with a frequency that is constant in time. Physically, if a state has a definite energy E at some time, then energy conservation tells us that the energy must be E at any later time. So when we have a superposition of energy eigenstates as in question 2, then no matter what time we are talking about, the state is still that same superposition of energy eigenstates.
 
To get a feel for parts d) and e), it's probably a good idea to play with the bound state simulator here:

http://phet.colorado.edu/en/simulation/bound-states

You can set up a superposition of energy eigenstates by clicking on "Superposition state", then setting c1=c2=1 and clicking "Normalize" and "Apply". The state is now a superposition of these two energy eigenstates, and you can watch the wavefunction or the probability density as a function of time.