1) Some sketches and simple calculations should be enough to answer this whole problem! (You don't have to rederive Gas. formulae if you don't want to...)

2) This is a good and important problem which you should put some time into thinking about. No calculations are required! You can usually sketch wavefunctions by thinking about general features - symmetry, number of nodes, curvature. Remember that curviness is related to energy. The sharper/curvier your function, the higher the energy, and thus the more tightly trapped. (Also, functions which decay away to infinity more gently are less tightly trapped, and have lower energy)

You know about wavefunctions for SINGLE wells, which may help too...

Note: when b=0, this means we have a single well, width=2a. (So, those sketches should be very easy!) When b>>a, the wells are far apart, and essentially independent. You may be tricked by the first excited state in this case though: remember, u2(x) always has one and only one node!!

b) For the energy, it may help if you imagine V0 is pretty big, so you're fairly close to an infinite well (then you know stuff analytically!) I want you to sketch the ground state energy E1 as a function of the well separation b (And then, on the same graph, also plot the excited state energy E2 as a function of b.) Be as quantitative as you can...

3) Before you begin calculating, just think a bit about this one; try to make a sketch or two of what the wave functions might/should look like, and then you'll be able to better recognize if your algebra is getting you the right answer. This problem is probably the toughest on this set...

4) I have done all the hard work for you here in class! Make use of the formulas from my notes, PP. 5-15 to 5-18, or Gas pp 94-99.

Back to this week's homework.