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Where do electrons go while making a quantum jump?

  1. Oct 25, 2008 #1
    I've always wondered this. Hopefully someone one knows. I always read the electrons jump, but they never say through what.

    thanx
     
  2. jcsd
  3. Oct 25, 2008 #2

    mathman

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    I am not sure what your question means. However when an electron goes from one state to another there is no inbetween.
     
  4. Oct 25, 2008 #3
    I thought it was quantum leak. As in leaking from one energy level to another.
     
  5. Oct 25, 2008 #4
    Electrons don't orbit. They are said to jump from one energy state to another and that jump is shown as a later where electrons are further or closer to the nucleus. If they are closer or farther away then they most have jumped through something.
     
  6. Oct 25, 2008 #5

    f95toli

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    No, because the were not "there" in the first place. Remember that we are not talking about classical objects here, electrons are not like tennis balls and usually they do not have well defined postions, their position is "smeared out" if you will (unless you somehow measure their position very acurately, but then their momentum becomes "smeared out" instead).
     
  7. Oct 25, 2008 #6
    Let's say we don't try to measure them. They then have a logical position. Where would they be and then do they jump? This metaphor seems very strong. People say they jump and that the different energy states map to position.
     
  8. Oct 25, 2008 #7

    ZapperZ

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    OK.. I don't measure the electron in the 1s orbital. Where is its logical position?

    Zz.
     
  9. Oct 25, 2008 #8
    >Zz

    Sorry to trouble you.
     
  10. Oct 25, 2008 #9

    f95toli

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    No, that is the point; they don't. Again, electrons are not "balls", you can't think of them as classical objects.
    Also, I don't know where you read about "jumps" but it is a very sloppy description best.
    We can -at most- talk about electrons making transitions from one state to another (e.g. a transition from the 1s state to 2s state); but that does not imply that an electron "jumped" from one position to another.
     
  11. Oct 25, 2008 #10
    The electrons don't jump anywhere, the state changes from one state to another. They need a verb to describe this and they chose "jump". Don't read too much into it.
     
  12. Oct 26, 2008 #11
    But there is! And the Schrodinger equation governs the dynamics of the transition of "between" states.
     
  13. Oct 26, 2008 #12
    Oh. Then where are the electrons?
     
  14. Oct 26, 2008 #13

    malawi_glenn

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    The reason why one calls it "jump" is that you draw an energy "ladder", and then on this ladder electrons goes up and down, in discrete steps = "jump". They never have an energy between those steps . http://cache.eb.com/eb/image?id=62996&rendTypeId=4

    They do not jump in ordinary space, but in energy space (an abstract space)

    (well the energy uncertanty relation holds, which relates to the lifetime of each energy state, but that is another issue than this one)
     
  15. Oct 26, 2008 #14

    ZapperZ

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    So far we have had 2 unverified statements about the "logical position", and now this. Can you please show where the Schrodinger equation actually show such a thing?

    Zz.
     
  16. Oct 26, 2008 #15
    Hi Todd. Quantum tunneling is indeed interesting conceptually. If we just look at the Schrodinger equation, it is obvious such a process is possible. But to understand it conceptually is another thing.

    One way to think about quantum tunnelling is by perhaps looking at the Schrodinger equation in the momentum space so we are dealing with energy and momentum instead of position and time. This way one may be able to think of quantum tunneling in terms of probability of a system with momentum say p to end up in a state of momentum P where P>p.

    This is conceptually appealing to me, but it cannot be done in general since one cannot take a Fourier transform of a general wave solution say psi(x)=exp(ikx) to obtain psi(p). However, one can show this is true if we have a simple harmonic oscillator. That is, the probability of quantum tunneling into the classical forbidden region is equal to the probability of measuring the state at E(forbidden) when say the energy of the state is at E0.
     
  17. Oct 26, 2008 #16

    ZapperZ

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    I don't see how "tunneling" is relevant in this case.

    In tunneling, there IS a probability for the particle to be in the forbidden region. In fact, I can manipulate the barrier by adding, say, magnetic impurities, without changing the barrier height/width, and that will affect the tunneling spectra. So this clearly shows that the particle did actually traverse through the barrier. This is NOT the case in atomic transition or any state transition where such a scenario of an "in between dynamics" is present. It doesn't.

    Zz.
     
  18. Oct 26, 2008 #17
    Alternatively, there are no quantum jumps between states, because the evolution of a quantum state satisfies a linear differential equation.

    Uh, then there's von Neumann's projection postulate, that when we measure properties of a quantum system the quantum state of the quantum system changes instantaneously. However, it is not the state of the quantum system that changes more-or-less instantaneously, but the macroscopic state of a thermodynamic system that is carefully tuned to make a thermodynamic transition between a metastable thermodynamic state and a more stable "click happened" state (then there's a feedback circuit to return to the metastable ready state). In other words, we can think of the jumps we observe as macroscopic thermodynamic jumps of the experimental apparatus, not as jumps of a quantum system that we can't understand.

    It's very clear that von Neumann's projection postulate is not an essential part of the interpretation or mathematics of quantum theory -- otherwise Everett-type and other no-collapse interpretations would not be possible -- and experimental verification of quantum mechanical models depends absolutely on statistics of ensembles of discrete events, not on individual discrete events, so it's best not to think there is such a thing as a quantum jump at all. If you can't think about QT without thinking in terms of discrete jumps, you need to re-tool. You can think in quantum jump terms if you want to, but be able to think in no-collapse ways as well.

    On the other hand, despite the smooth evolution of quantum states there is discrete structure to be found in quantum theory. Thinking in terms of a simple classical wave analogy, the oscillations of a drum skin are continuous; however, the boundary constrains the oscillations so that we can have any amplitude of each of the discrete resonances. There is an effectively discrete constraint on what continuous oscillations are possible. As time goes by, the amplitude of each resonance decays smoothly (the decay rate of each resonance is different, so the sound changes over time, ...). Disanalogy: a better model of the drum skin would take nonlinearities into account.

    Discrete structure is considerably harder to come by when we try to think in quantum field theory terms.
     
  19. Oct 26, 2008 #18
  20. Oct 26, 2008 #19
    Either there's a tunnel somewhere, with a ladder in it, that electrons go to while leaping and jumping when they aren't being smeared around, or quantum mechanics deals with probability amplitudes.

    After addition of energy to the system there is a nonvanishing probability of finding an atom in either energy state; a superposition of states. The popularized terminology of "leaping" is very misleading.
     
  21. Oct 26, 2008 #20
    Phrak,

    The answer to your question depends on your formulation of QM. In the de Broglie-Bohm or stochastic mechanics theories for example, the electron is a particle that moves in a definite, continuous trajectory during a "quantum jump"; and you can calculate that trajectory. Other formulations like GRW or MWI gives different answers.
     
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