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  1. SamRoss

    Any good education journals, magazines, etc.?

    It sounds to me like no insightful conclusions were reached because the experiment was not designed to garner any. Teachers were not testing out any new, interesting strategies - they were just doing what they normally do - so of course the only difference between the two classes ended up being...
  2. SamRoss

    Any good education journals, magazines, etc.?

    Pardon my face slap. Yes, you're right - one experiment with two classes could not be taken as rock-solid evidence. Ideally, the experiment would be run again and again with the same teacher, at the same time of the day, in the same environment, and so on in order to eliminate other factors. Or...
  3. SamRoss

    I Seeking better explanation of some quantum stats formulae

    In "Introduction to Quantum Mechanics", Griffiths derives the following formulae for counting the number of configurations for N particles. Distinguishable particles... $$ N!\prod_{n=1}^\infty \frac {d^{N_n}_n} {N_n !} $$ Fermions... $$ \prod_{n=1}^\infty \frac {d_n!} {N_n!(d_n-N_n)!}$$...
  4. SamRoss

    Any good education journals, magazines, etc.?

    Thanks very much. This is just what I've been looking for. :) That's true, but it doesn't mean there's nothing to be learned from investigating. If Class A was taught some material using Strategy A, and Class B was taught the same material using Strategy B, and 70% of Class A ended up mastering...
  5. SamRoss

    Any good education journals, magazines, etc.?

    Agreed. Learning in general is an interesting subject, but in my experience, discussions and articles on this topic tend not to be of much practical use. I am after the answers to very simple and specific questions. Some examples: Are students better able to answer percents word problems by...
  6. SamRoss

    Any good education journals, magazines, etc.?

    Much appreciated (although actually I've been here for quite some time). I won't get into it here, but I have a great deal to say on this topic. I'll probably start a thread on it in the near future. Those appear to be related to medicine, but I appreciate the response.
  7. SamRoss

    Any good education journals, magazines, etc.?

    I had to suffer through a lot of pseudo-science to earn my master's in education. I am suffering through more of it now while I "study" for my administration license. In fact, because anachronistic theories such as VAK (visual, auditory, kinesthetic learners) get floated around so much in the...
  8. SamRoss

    B Uncertainty versus impossibility of measurement

    I didn't know this. Thank you. I had been assuming that if it were possible somehow to make a measurement of position and momentum then both of those measurements would be exact even if they were unpredictable beforehand.
  9. SamRoss

    B Uncertainty versus impossibility of measurement

    Have I spoken too soon? Here's a quote from pg. 19 of Cresser's Quantum Physics Notes: "However, the uncertainty relation does not say that we cannot measure the position and the momentum at the same time. We certainly can, but we have to live with the fact that each time we repeat this...
  10. SamRoss

    B Uncertainty versus impossibility of measurement

    As far as I'm concerned, my original question has been answered satisfactorily by you and others. The HUP does not tell us that we can't measure the position and momentum at the same time but there are other reasons why we cannot do so. I do not have any outstanding questions at the moment; I...
  11. SamRoss

    B Uncertainty versus impossibility of measurement

    I read the section you recommended, 4.3, which had to do with the double-slit experiment and a quantum eraser. It was an interesting discussion about how knowledge of a system results in the loss of interference but I'm not sure how it ties into this discussion. Did I read the wrong part? The...
  12. SamRoss

    B Uncertainty versus impossibility of measurement

    So there is a "disturbance" inequality which is separate from the standard HUP?
  13. SamRoss

    B Uncertainty versus impossibility of measurement

    1. If I understand your posts correctly, the problem with measuring position and momentum simultaneously does not have to do with the HUP. Instead, simultaneously applying the techniques normally used to measure position with the techniques normally used to measure momentum does not result in...
  14. SamRoss

    B Uncertainty versus impossibility of measurement

    Having measured A’s polarization at angle X and B’s polarization at angle Y, it would seem like we have enough information to predict the outcome of an experiment measuring either A at X or A (same particle) at Y. However, this should not be possible though I’m not well-versed enough to state...
  15. SamRoss

    B Uncertainty versus impossibility of measurement

    I do not believe your second statement follows from the first. In fact, this is what my whole question is about. The statement "The outcome of the measurement cannot be predicted with certainty" is often taken to be synonymous with the statement "The measurement cannot be made precisely". But...
  16. SamRoss

    B Uncertainty versus impossibility of measurement

    The uncertainty principle tells us that there is no state that a particle can be in such that we can predict with certainty both what the result of a position measurement will be and what the result of a momentum measurement will be. This statement is not the same as saying we can't measure the...
  17. SamRoss

    Not sure where this final Hamiltonian came from

    Oh okay, it wasn't that bad after all. I suppose it was. Finding the eigenvectors was apparently unnecessary for finding H. Thanks everyone!
  18. SamRoss

    Not sure where this final Hamiltonian came from

    Here's the problem and the solution provided online by the author (the problem numbers are different but it's the same question). I think I'm okay up until the last step where he declares the Hamiltonian is (1 1 1 -1). Where did he get those components?
  19. SamRoss

    What are the coefficients of psi_n for this state?

    #vela #DrClaude #TSny #PeroK Okay, I think I got it. There are two A constants - one was for ##\Psi## and one was for ##\psi##. Thanks for your help, everybody!
  20. SamRoss

    What are the coefficients of psi_n for this state?

    #vela #DrClaude Thanks for the responses. ##c_n = \frac {1} {\sqrt2}## seems reasonable. I'm still confused about the general method for finding A and ##c_n##, though. A few pages back, Griffiths introduced the potential energy function for the infinite square well, V(x) = 0 if x is between 0...
  21. SamRoss

    What are the coefficients of psi_n for this state?

    I am working through David Griffiths' "Introduction to Quantum Mechanics". All of the solutions are provided online by Griffiths himself. This is Problem 2.5(e). I understand his solution but I'm confused about one thing. After normalizing Ψ, we find ##A=\frac {1}{\sqrt2}##. Griffiths notes that...
  22. SamRoss

    I Is my solution to Buffon's needle OK?

    Buffon's needle was presented as a problem in David Griffiths' "Introduction to Quantum Mechanics". In the book, a needle is of length l is dropped randomly on a sheet of ruled paper with the lines of the paper also a distance l apart. It is required to find the probability of the needle...
  23. SamRoss

    B Is my intuitive way of thinking about non-Euclidean geometry valid?

    I added both books to my wishlist. Thanks for your help!
  24. SamRoss

    B Is my intuitive way of thinking about non-Euclidean geometry valid?

    Perfect! Thanks. If I like the first book, I'll definitely be buying this one.
  25. SamRoss

    B Is my intuitive way of thinking about non-Euclidean geometry valid?

    I seriously doubt that. Anyway, I just ordered a copy of "Elementary Differential Geometry" by Barrett O'neill. This will be my first book devoted specifically to differential geometry. Let's see if that helps!
  26. SamRoss

    B Is my intuitive way of thinking about non-Euclidean geometry valid?

    I am familiar with undergraduate math and special relativity. I have read all of Susskind's Theoretical Minumum books. In fact, I have even read through Einstein's orginial papers on special and general relativity. I know the basic ideas. "Distance" is measured in proper time (being invariant...
  27. SamRoss

    B Is my intuitive way of thinking about non-Euclidean geometry valid?

    #PeroK #Orodruin Can you recommend a beginner-level book on differential geometry? My main motivation is to understand GR.
  28. SamRoss

    B Is my intuitive way of thinking about non-Euclidean geometry valid?

    A straight drive means stepping on the gas while keeping the steering wheel centered. Two drivers are parallel when they are pointing in the same direction from the point of view of an observer in three dimensions. A line is a collection of points in three dimensions such that a vector between...
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