Please send us your questions about anything class-related - this week's homework assignment, course content, course administration, or whatever. We will either email an answer to you directly, or if we think the question might be of general interest, we will instead post the question and answer on this page instead, with your name removed. So check this page periodically to see what questions your classmates have asked!
Please email us at Steven.Pollock at colorado.edu or Oliver.DeWolfe at colorado.edu with "Phys3220" in the subject line of your email!
Survey questions:
Most people who filled in the participation survey had a question. Here I tried to answer all of them!
Homework 4 question:
Prof Pollock and/or Prof DeWolfe,
I have a homework question on 2d. I've found <E> ... and I think it is correct. My uncertainty in energy, however, is appearing to be less than <E>-E_2, which seems incorrect. I thought that sigma should be EXACTLY equal to the difference between the average and the two points because there are only two discrete points.
Did I phrase that well enough that you understand what I'm saying?
So is my intuition about what sigma should be for two discrete points incorrect or have my calculations gone aloof?
Yes, you phrased it clearly (to me!) and I do agree with your intuition about sigma... (I gained confidence in that particular intuition in the Tutorial a little over a week ago!)
So this would lead me to suggest that you double check your calculation of <H^2> (and thus your uncertainty in energy) You didn't email me your work, but it sure seems like you must have made some mistake there.
P.S. It's great that you thought to check in this way, very nice! It's a theme in this course that quantum calculations can sometimes get a little involved, and so we want to build as much intuition as we can to let us check results, just like you did here!
LHC rap?
I'm taking Plasma Physics this semester and Prof. Parker told us about this video. http://www.youtube.com/watch?v=j50ZssEojtM
This video has cheesy rapping and physics all in one, and there is even a moment when spider-man makes an appearance.... I thought you might appreciate this as much as we did in plasma.
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Homework 2 clarification:
Professor Pollock - In 2.3.c what do you mean by the 'classical frequency of the motion of the Bohr model?' Do you mean the frequency at which the electron is orbiting around the proton. Thanks,
Yup, that's what we meant. So, f=cycles/sec, i.e. revolutions/sec of the electron around the proton.
(Or I suppose you could find omega in radians/sec, if you want "angular frequency". Just a 2 pi difference, and you need to be consistent when you check the correspondence principle!) -Steve
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Lecture note questions/clarifications:
Q1. What experiment(s) proved conclusively that Einstein's theory on "hidden variables", the realist position, was incorrect? Your notes, and Griffiths excludes the specifications.
Q1: The experimental disproof of local hidden variables comes from measurements of Bell's Inequalities. (These were derived theoretically in '64, but the first experimental checks were in the 80's, there have been many more since then) At some point this semester (though I suggest you wait a bit, it will make much more sense after a couple more months) you should read Chapter 12, particularly 12.2, to get a pretty rigorous explanation. There is a "catch", but Einstein would not like it - you can still have hidden variables, but then you are experimentally obligated to accept non-local interactions, what Einstein would call "spooky action at a distance". (These non-local interactions do not violate special relativity, but they sure feel... spooky) So the right way to say it is that no *local hidden variable theory* is consistent with these experiments (even in principle, the details of such a theory are not relevant)
Q2. pg.18 of your notes. With F=-kx, and x''(t) = - omega^2 * x(t) implies that k/m = omega^2 somehow? (right?)
Q2: Yes, I should have defined it, but it's pretty conventional - as you observed,
omega for the simple harmonic oscillator is defined to be Sqrt[k/m].
So, you can write F=ma as m d^2x/dt^2 = -k x,
which gives d^2x/dt^2 = -(k/m)x.
Defining omega^2 = k/m makes this equation look simple:
d^2x/dt^2 = -omega^2 x,
which you can solve by inspection (?) and get sin and cos of (omega*t), i.e. the usual simple harmonic oscillator solutions.
Correction. On page 14, the last equation on has a '=' sign in it rather than an intended '-'.
Thanks, fixed the typo!
Steve
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Pi
For those of you who are Pi fans (which I recall from last Mar 14), check out this article from an old friend of mine, pi is wrong!
-Steve
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Steve - I know you haven't seen "What the Bleep do we Know?", but I thought you might like this anyways. Most of that movie is just a bunch of people talking about our thoughts changing the shape of water molecules and stupid things of that sort, but every now and then the movie will do an animation that tries to explain some actual physics. I thought you might like some of these animations. The animated physicists name is Dr. Quantum. Here is a link to my favorite, the Double Slit Experiment. There are a couple others easily found by searching "dr quantum" on youtube.
http://www.youtube.com/watch?v=DfPeprQ7oGc
This is the five minutes of that four hour movie that is actually good, so thank me for saving you a lot of time.
Thanks indeed for saving me from watching 4 hours (!?) of that movie :-)
Nice animations - I agree - it's not bad to explain some of the basics of wave/particle duality. Although they are working hard to make this more mysterious than it needs to be. This focus on the "electron knowing it is being observed" at the end (with possible implications about consciousness maybe having to do with it) is a little disingenuous. You just need to think about the *physics* of observation, quantum collapse occurs through the interaction of particle with an observing mechanism. Observing an electron requires an interaction, e.g. scattering something (probably light) off the electron. And of course, that interaction has an impact on the electron - photons carry energy and momentum in a well-defined way. So the change in the interference pattern is to some extent understandable physically by thinking about the consequence of exposing electrons to the observing device (i.e. they are now interacting with photons as well as just the slits).
I have another quibble - earlier on, they make the 2-slit interference pattern (the multi-band pattern) for particles (or even waves) seem crazy/stunning, (which I suppose it sort of is) but they got the physics just a little wrong, and this makes that craziness seem much stranger than it needs to be. To get the multi-band pattern, the waves from EACH slit must be diffracting enough to interfere with each other off to the sides in the pattern. But that means that the SINGLE slit pattern would NOT be such a sharp band, it too would be spread out well across the screen. So at least in that respect the interference isn't so nuts - the waves are spreading out from each slit and heading to all portions of the screen, where they can interfere with each other. In the animation, the original single slit pattern looked highly localized. You *could* make that happen (with a wider slit, e.g.) but in that case you won't observe the double slit interference very easily, if the two sharp single patterns are well separated. So they have sneakily changed the slit size between the two experiments on us, without admitting it!
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