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So, I finally have a question. It's more of a comment.

I have decided to treat this class more like a math class than a physics class. The concepts are so far out there that I will have to reverse my usual thinking. Normally I try to focus on understanding, and from there the math comes more easily, and any required memorization will be easier as well. Here, I think that process would be way too slow. We have a scant few weeks. For me, anyway, the understanding will take longer than that, if it ever truly comes, and I have exams to take that are more math than anything else.

I guess my question would be does anyone see anything wrong with this idea? Is it a good idea?

I think there's wisdom in your idea however I believe it will only provide you limited improvement. Consider the first quiz. At first glance it appears to be heavy on the mathematical computations but at second glance some of the math can be bypassed. For example the first problem, Prof. Kubota stated, “guesses based on sound physics intuition to simplify your calculations are encourages” and indeed the problem can be solved with little to no math. Without the understanding all your are left with is the math and memorized equations which can leave you stranded. But, I suppose having a strong understanding of the math and memorized equations and a weaker understanding of concepts is better then a weak understanding of all of it!

I was going over mondays lecture and was wondering how did we get D=-A and C=-B? was it just the fact that we were looking for odd solution which is Antisymmetric? and since we know this we could eliminate some unknowns this way. and another thing is that the imaginary k still bothers me a little and it came up today as well. what does it really (physically) mean to have an imaginary p?

I also have this general question…I think it's something to do with the fact that we can have E > 0 and E < 0, and the boundary conditions for these cases, giving us the two options of C = +/- B, but I'm not very sure on that.

one more thin; we say that because the potential is symmetric we can reduce the problem and look at the continuity of psi and its derivative only at one point (a or -a). would this work if the potential was -V between 0 and 2a rather than -v between a and -a. (and 0 everywhere else) ?

In response to your first question, the reason we chose C = -B and D = -A is mostly in part to symmetry but also we were looking for the odd solutions of the finite square well. Had we stuck with even solutions then C = B and D = A.

In response to your last question, I think that you can only use symmetry to reduce the number of variables when you're looking at +a and -a. If you're looking at a function which is symmetric but it's not centered at zero, you'd want to shift your variables so you have the function centered, so you can take advantage of the symmetry.

As far as imaginary p goes, I think of it like the particle is in 'tunneling mode'. If it were behaving classically, it could not enter such a region at all, but since it has its 'imaginary p' it has a chance of passing through a classically forbidden space by tunneling through it into an allowed space.

For example, in the step potential problem we did for homework, the particle had some amount of wavefunction which penetrated into the barrier. The particle still couldn't be observed in the barrier, but if the barrier were narrow, there could have still been a nonzero value of <math>\psi</math> on the far side of the barrier, thereby allowing tunneling.

I don't think about p and just try to look at <math>\psi</math>, remembering that only <math>\psi^2</math> has any physical meaning.

Why is the scattering problem inherently asymmetric? Why does the wave only come in from one side only? Do scattering problems have even and odd functions? If so what are some examples? How can they be identified?

To answer the question of why the wave comes in from one side is because the scattering problem is based on a wave coming into contact with a barrier. This can only occur if you define an origin of the wave outside of said barrier.

I am interested in figure 2.19. We can see that at certain energies the transmission coeffiecient is 1, while in the energies between them the transmission coefficient is less than 1. Is this property useful for some practical applications?

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