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    Negative kinetic energy in tunneling

    Because eigenvalues of an observable, namely momentum, becomes imaginary then.
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    Negative kinetic energy in tunneling

    There's indeed such a problem. In regions where energy of particle is smaller than the minumum of particle, the solutions are exponential rather than oscialating, and kinetic energy operator becomes negative. For instance, (in nuclear physics) in a spherical potential well, the solution in the...
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    The Heisenberg Uncertainty Princeple

    See 3.3 and 3.4.3 in Griffiths.
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    Free Math Textbooks

    By now, it's up.
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    Heisenberg and quantum mechanics

    Ouch! Sorry! I'm not a native English speaker, that's probaby why an quite-ambioguous sentence turned into disaster in my hands! Hmmm. Right. But then, the width of slit isn't measure of it's position at the instant of momentum measurement. Let's see what I've understood from your...
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    Heisenberg and quantum mechanics

    Wow, that's whom I'd call a braveheart. Fine, but which is the last word? BTW, there should be limitations on your CCD (and our technology) by uncertanity principle, so I suppose it's impossible to make a device that measures momentum of a particle with perfect accuracy. Err.. something...
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    Why does an observer affect the electron?

    Though I'm aware of HUP is talking about standard deviation, I'm curious about one thing. So I'd like to raise this question: in what precision can we measure position and momentum of one, single electron. Feel free to talk in terms of eigenstates and wavefunction collapse.
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    Matrix mechanics

    For someone who's bored with wave mechanics, would you suggest studying Heisenberg's matrix mechanics (which was the first formulation)? Are there any major/conceptual differences? (except one talks about waves and the other doesn't!) And for someone who wants to study it, what books/online...
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    Dirac's K

    Horray! :approve: Huge thanks, finally Schrödinger equation did come out! One last question, how could you (or Feynman) see which term you had to expand? I rather tried expanding e^{iLdt/\hbar} directly, without expanding the potential term around a fixed point, and without leaving a...
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    Dirac's K

    Ups. I missed that bit. So my A became A \sqrt{\frac{\pi}{-im/\hbar \epsilon}} = 1. V(x') \frac{\partial^2 \varphi}{\partial x^2}... term is dropped since it has an second order \epsilon. OK, by doing so, I had the potential term nicely, but I still have a weird extra coefficent in the same...
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    Schrodinger's Equation

    Hmm. How about this: Following (Fourier transform) holds for any wave packet \psi(x,t) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} \phi(k) e^{i(kx-wt)} dk Let us assume that matter is a kind of wave, so obeys this equation. Now, to relate the wave with quantities we all know and love, we...
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    Dirac's K

    Thanks for the reply! I didn't know the bounds are infinities... Also, I couldn't get \lambda to the 3/2th power, for -iV'(x') y \lambda, but as you did, I used only the first term for potential. Anyway, I couldn't see how Schrödinger equation comes out from what you've written, so I've tried...
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    Localization vs De Broglie wavelenght

    What i mean is this: if you have a "piece of wave" that is too short -such as a sudden small bump-, would you call it a wave? To talk about a wave, you'll need a wavelength, roughly. (Of course, if you're pedantic, you actually need something that is periodic, but one-wavelength piece is fairly...
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    Localization vs De Broglie wavelenght

    I think your teacher's statement was rather "intutive". (Note that he seems to be talking about a precise wavelength, no \Delta \lambda is involved. That'd mean a precise momentum). More likeky, his pointly was this: if you have a minimal thing that would represent a wave, maybe a pulse or a...
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    Localization vs De Broglie wavelenght

    Yup. p = \frac{h}{\lambda} then, by differentiating both sides \Delta p = -\Delta \lambda \frac{h}{\lambda^2} But I see no point in messing with \Delta \lambda. Your teacher is talking about \lambda. Also note that these deltas can be quite misleading. What Heisenberg means with "uncertainty...
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    Dirac's K

    In" [Broken], he mentions this: I'm trying to get the same result, but I'm stuck. Has anyone done this before?
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    Entropy and time reversal

    I guess you can live without believing irreversible wavefunction collapse. Following Feynman's example, increasing entropy is a consequence of statistical behavior.
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    Euler force

    It should be something like this: suppose you're standing on a disk initially at rest. Then it starts to rotate, say clock-wise. At that time, the (inertia-)force you feel that is pushing you counter-clockwise is Euler force.
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    Euler-Lagrange equation for paraboloid plane

    I have a classical mechanics question I couldn't conclude. The reason seems to be mathematical. It's this: There's a paraboloid shaped plane of mass M, which is standing on a frictionless surface and can slide freely. It's surface is y=ax^2. A point mass m is place on the plane. Solve the...