Did problem 4 work out for you? Did problem 5 make sense? Were you able to glean anything from the requested graphs (b or c)? Did you resolve what to calculate for 5d? Did that calculation work out okay? Were you able to get a simple result for 6? What was it? Were the issues related to conjugation of \(\psi_{21x}\), \(\psi_{21y}\) and \(\psi_{211}\) worked out to your satisfaction?
Anyway, those are some questions, and I am interested in any comments you have on this or anything else. General comments are welcome here.
Added Sunday at 1 PM:
Here is what I got for HW5, problem 5. I did not get around to doing the integrals yet, but you can see how the two parts of the problem, time dependence and spatial integrals, can be separated. Breaking a problem into parts like this can allow you to do much harder problems. You can see here how the essence of the problem emerges even before the integrals are completed.
Keshav, a good friend of mine, brought up this general question about quantum mechanics that I find very interesting.
ReplyDeleteMost of the time we use probability & statistics to help understand situations where there are unknown forces controlling the situation. This doesn't seem to be case for quantum mechanics, ay?
Take the double slit experiment: is it that (1) there may be other factors we don't know yet, 100% determining where the electron goes in the double slit experiment, so we just employ probability and statistics as a model? Or (2) is probability & statistics the ground-level, hardwired in physics?
One way to think about it: If I had a deck of cards, for example, and I flip over the top card and look at what it is, successively, for each card I take out, there is a probability I get a king or a queen, etc. At the end, when all of the cards are flipped, if I could rewind time and maintain the data I took, I would know exactly which cards will come out when. I will have completely understood the system.
So in the same light, if I rewind time after the double-slit experiment, will the electrons go to the same fringes in the same order? Or, again, is probability & statistics hardwired in physics?
Or another way to put it, maybe: since all the probability seems to come from the Heisenberg principle – can it ever be defeated?
Interesting thoughts
DeleteCould you maybe elaborate questions 4 and 5 in a video/blog post? I felt like I needed more discussion on them to really grasp the situations at hand.
ReplyDeleteI feel like that's a good idea. Could you also do that for question 6 as well?
DeleteI 'third' said motion.
DeleteI can do that. For 4 I think I understand what you want. For 5, some feedback would be really helpful for me. How far did you get with 5? What did you calculate for 5d)? What did it show you?
DeleteIn regards to problem 5, I feel like I'm not (fully) convinced the first two graphs were really the same (when I calculated psi^2 for each of those values of time, my cos term changed sign). I also read somewhere (albeit for the finite square well) that the cos term changing sign gives rise to the wave function being mostly on one side of the well. I may be terribly confused. Either way I'd appreciate a discussion on this matter. For 5d, I calculated the expectation value of x^2, primarily because the integrands would be even and therefore not integrate to zero. This showed me that is time dependent - working on delving deeper now. Thanks in advance Zack.
Delete@killaW They are not the same. The point is that they are different.
DeleteWhat you read applies to the superposition of a gs and a 1st exc state. It is not general at all.
Ah well that explains a good amount, thanks for posting.
DeleteI am redoing all the problems in homework set number five because last week was very hard on me. I did not have enough time to properly do the homework set. Professor Schlesinger, when is the answers to Homework set number five going to be posted? I would like to see if I am doing the homework problems correctly.
ReplyDelete