Please comment here regarding and thoughts, questions, ideas or results you have for these problems.
9. For a system of 4 identical attractive square wells that are equally spaced and pretty close to each other but not touching,
a) sketch the ground state.
b) sketch a few excited states.
c) How did you construct those states? Discuss. What would come next (in terms of states)?
10.
a) For a double well (2 identical attractive square wells that are
pretty close to each other but not touching), show that for some
separations the states come in pairs. What is the nature of those pairs?
Discuss qualitative aspects of their construction and energies.
b) What is the analogous thing for a quadruple well (as in problem 8)? Discuss.
For 9 a) We did this in class but basically what we did for the ground state was use the wave for one square well and connect it four times with the ends extending in between the regions of the wells.
ReplyDeleteb) The first excited state will have one node at the center and to get one node and keep symmetry we can flip half the wave function form part a upside down.
c) The first ground state we drew because we know how it looks for one square well which is just Y(x)=ASin(kx). Anyone know about the higher states?
10) a) ? dont know yet but I would say that for very small separations maybe the waves overlap more and more, and thus come in paired states.
b) I would guess that for 4 wells we would have the states in pairs of 4.
Let me know what you guys think!