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I took 2 courses on Quantum Mechanics during my undergrad and I'm taking the Coursera course now as well for fun. My biggest quibble with how QM is presented i

• andrewcooke 14y ago
  yeah, but this is more general than qm - it's amusing to ask (other) physicists how fast electrons move in typical wires (a purely classical number, but most won't have a clue).
  • jules 14y ago
    It's not exactly clear what you mean by "velocity" in that question. Drift velocity? Fermi velocity? (and others) These two differ by multiple orders of magnitude, so it's easy to wrongly conclude that another physicist doesn't have a clue. Intuitive explanation: drift velocity is the overall streaming velocity of the moving electrons, fermi velocity is the velocity of a single electron. The reason these are different is that electrons move back and forth heavily, thus the fermi velocity is high. But under normal voltages, they move just slighly more in one direction than the other on average, which is the drift velocity. Of course this is highly simplified, and the real story is quantum mechanical.
    • andrewcooke 14y ago
      maybe i'm being over-sensitive here, but it really feels like you're making excuses and trying to hide behind details. surely it's obvious i mean drift velocity from the context (how can you call fermi velocity classical?). i don't want to drop names, or pull rank, or argue from authority, but this comment is based on memories of a happy afternoon chatting with other students. none of them said "oh, i don't understand, do you mean drift or fermi or one of the many other velocities i can think of?" instead, to a man or woman they said some random large number than stared, then did the maths, and then burst out laughing. they were smart people. and i admit i was one of the dumbest (and i didn't come up with the question - i can't remember who did). and none of them felt the need to make excuses or smokescreens about learning something new.
      • jules 14y ago
        I didn't read the "(a purely classical number, but most won't have a clue)" as being part of the question, but rather as commentary about people answering the question. Also "how fast do electrons move" does really suggest the velocity of an electron and not the net average velocity...anyway, calculating drift velocity is easy. From the current and the charge of an electron, calculate how many electrons are passing through the wire per second. Then calculate the number of electrons in the wire from the material properties. The answer is the ratio between these two, multiplied by the length of the wire. Since this contains many numbers that most people (even physicists) don't know off the top of their head (density & weight of copper, avogadro's number, electron charge) this is a bit hard to guesstimate within an order of magnitude without looking things up, but it will be a small number of meters per second.
• gus_massa 14y ago
  I suppose that most of the time you are drawing the probability density (|phi|^2), but in a few case you show Re(phi) and Im(phi). It looks a little to wavy. For example, if the initial state of a free particle is a (real) Gaussian distribution, after a time it should still be a wider Gaussian distribution (with the wave function phi modulated by a complex phase). I think that this is due to a problem in the numerical method. In spite of this, the general behavior of the simulation looks right. For example, in the harmonic oscillator, if the initial configuration is a well localized state, after 1/2 period the configuration should be a well localized distribution on the other side of the parabola, and this exactly what the simulation shows.
• Dn_Ab 14y ago
  Cool demo. Interesting questions. There are nobel prizes waiting for the answers to some of them. Warning: The following is not precisely target at your post. The core of some your questions are the kind answerable only with mu. Essentially, you are asking for some physical intuitions to relate the quantum world up to the world as we see it. But the thing is that there is very little in our macroscopic reality that relates to the quantum world. All analogies are broken. Here's the key thing to realize. Quantum mechanics is hard not because it is complex =). Far from it. It hard because we have no mental basis with which to represent its concepts. The opposite should hold too. A Quantum intuition would find our world bizarre, very hard to understand and - unlike how we feel about QM - justifiably complex. But if one takes a multicultural appreciation approach to how systems evolve, QM becomes a bit less offensive to one's sensibilities. The only path to approximate intuition is to drill the math and think about the concepts. Simulations are another great option. They allow one to create a rope bridge from the math to something that feels a bit more concrete. Still not intuitive but better than nothing. The idea is to get to the point where you can use the math as a map. So you won't ever be able to feel as comfortable with it as galilean relativity but you can form questions, think about reality and use the map to guide your mind. I am the opposite of you - I think a lot of the physical or incidentals of experiments are useless baggage for building that map. What does a particle with some particular wave function look like? At this point it is not useful to think about how things look. Focusing on what things "look" like would again be just be a rough analogy, possibly misleading (similar in spirit to focusing too much on tangent lines for derivatives) and might create a false crutch by waylaying the brain from becoming more comfortable with the abstract surroundings. And then there is the question of: is the wave function? Does it make sense to think of it as something physical? (I don't think so). Does it occur on scale of nanoseconds? Seconds? Hours? While kinda opposite in direction to your questions, work on decoherence is answering some questions of timing. But nothing will shed light on entanglement, coherence and aspects of measurements better than quantum computers. Lets hope they get invented soon or less preferably, proven not to be possible. Each would learn us a lot.
• drostie 14y ago
  There is an advantage to the original formulations of QM and they are precisely these. It's true that in Quantum Field Theory you don't see these Bell Inequality ideas and I've seen people working in Quantum Information theory who struggle to prove that you can multiply a wavefunction by an arbitrary phase factor and it is an unobservable change. QFT has real current statistics and Lagrangian densities and Feynman diagrams, which give you a much more tangible feel of what physics you're describing. In my experience it is just another math course and there is no Physics anywhere. Heisenberg equations of motion are a good place to start. The original way we stumbled upon quantum mechanics was due to Heisenberg, who noticed that a lot of the wavy stuff people wanted to explain could be explained if Hamilton's equations of motion df/dt = {f, H} + ∂f/∂t were generalized by treating x(t) and p(t) as matrices and insisting that they do not commute, leaving instead [x, p] = i ħ as a matrix version of an "uncertainty principle." The corresponding quantum equation for an observable  is that dÂ/dt = i [Ĥ/ħ, Â], which allows you to start (most famously) with a harmonic oscilator Ĥ and derive the Hamilton equations dx/dt = p/m, dp/dt = - k x, precisely due to the failure of x and p to commute. So you get this direct connection between known physics equations and the quantum theory, and often the same thing which is responsible for driving the uncertainty relation also drives all of classical physics. What does a particle with some particular wave function look like? |Psi|^2 in the appropriate basis, I should say. As it evolves in time it "smears" out according to the time evolution equations, but how fast is the process? Does it occur on scale of nanoseconds? Seconds? Hours? In quantum mechanics there is a discrete energy level spacing ΔE, and the answer is that no observable can change much faster than ħ / ΔE. For the harmonic oscillator for example, nothing can change much faster than 1/Ω by this criterion. What exactly is an example of a measurement? This can get a little touchy but a good example is a photon hitting a photomultiplier tube and generating a click -- especially if you start to play with the polarization of the photon to generate entanglement and so forth. Edit: With all that said, I highly recommend watching Feynman's New Zealand lectures which explain, among other things, why CDs show rainbow patterns (in a time, sadly, before people had CDs and so Feynman kind of just says "I wish I could have brought you an example.") http://vega.org.uk/video/subseries/8 http://vega.org.uk/video/subseries/8
  • Dn_Ab 14y ago
    You're right. And it's well explained despite the subtle jabs at Quantum Informations theory =P. There are definite advantages to the physics focused approach. As a physicist (which I am not), in your practice of QM you get familiarish concepts like spin, momentum , oscillators and Lagrangians. But despite the wild successes of QFT, when it comes to explaining things it is extremely hard to do without either using broken analogies or talking about Feynman diagrams, Lagrangians and Hamiltonians. To realistically depict what is going on you are replacing one branch of math with another more complex branch with the main advantage being that someone who has learned the math of classical mechanics can have a slightly stronger physical intuition. The advantage of QIT is that because it is relatively simple already, a slightly simplified form is still easier to understand and more representative of the real thing than a highly simplified explanation of QFT. The other advantage of this is that the simplicity allows the raw structure to be exposed and tackled much more readily. If I would bet I would say answers to questions like what is the wave function exactly , how does the macroscopic universe arise from the cloudy quantum picture, what is really going on in measurement etc will come from QIT. I get the impression that many physicist don't have much respect for foundations but these questions are still worth answering and would have a practical effect on our world right away. QIT is young yet, there are advantages to being able to take multiple viewpoints of the same thing. The correct viewpoint can vastly simplify a problem. To quote Egan: " Everything becomes clearer, once you express it in the proper language."