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I Source of energy for quantum tunneling of a particle

  1. Dec 19, 2017 #1
    If a micro-particle tunnel through a barrier which has higher potential energy than the energy of the particle, then from where does the particle get the energy to cross that barrier?
  2. jcsd
  3. Dec 19, 2017 #2
    That's the point of tunneling: it doesn't need the energy to cross the barrier. If it did have, it would just cross the barrier classically.
  4. Dec 19, 2017 #3


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    At some point in time, we observe the particle on one side of the barrier. At some later point in time, we observe the particle on the other side of the barrier.

    QM is silent about what the particle "really" does between observations; in particular, about whether the particle was "really" inside the barrier itself.
  5. Dec 19, 2017 #4


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    One interpretation, which is more-or-less standard, is that the particle does not "cross" the barrier, but simply appears on the other side without ever being in the barrier itself. In the Bohmian interpretation of QM, the particle travels across the barrier and needed energy comes from the quantum potential. If you want an answer that does not depend on interpretation, then see the answer by @jtbell above.
  6. Dec 20, 2017 #5


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    Now occurred to me that wave function does not vanish in the barrier, so there is a finite probability for the particle to be found in the barrier. How is it consistent with energy conservation? The answer is that, in this case, it is the measurement apparatus (that measures position in the barrier) that gives the particle extra energy. This is one more demonstration of quantum contextuality, that is the fact that measurement does not merely reveal the preexisting values of observables, but changes the properties of the measured system itself. Measuring position in a state which is initially an energy eigenstate is very much analogous to measuring spin in x-direction in a state which is initially an eigenstate of spin in z-direction.
  7. Jan 5, 2018 #6
    When the tunnelling particle is an electron, recent experiments have shown that its path, or imaginary path, are curled by a magnetic field and so the electron behaves just as though it was a real electron in vacuum. Other experiments have shown tunnelling electrons are subject to electric fields. Neither of these results suggests a real particle was in the gap, but rather that the wave function must take into account magnetic and electric fields, and I suppose gravity too, in order to predict where the / an electron will emerge (if one knows where it entered).
  8. Jan 5, 2018 #7


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    Could you refer to original papers about this experimental findings. I don't understand what you mean.
  9. Jan 5, 2018 #8
    Sure, here is one reference I have on hand;

    Focusing of tunneling electron in a magnetic field
    • a Department of Physics, Waseda University, 3-4-1 Okubo, Shijuku-ku, Tokyo 169, Japan
    • b Nanoelectronic Materials Group, Frontier Research Program, RIKEN, Hirosawa 2-1, Wako-shi, Saitama 351-01, Japan

    Received 16 February 1999, Accepted 8 June 1999, Available online 25 January 2000
    It is well known how an electron is bent by a magnetic field, but it is not known how a tunneling electron is bent by such a field. We conducted an analysis of how the electron is bent by the field using a Euclidean path integral method. As a result of this analysis, we make it clear that the electron is bent by Lorentz forces, as is an electron that does not tunnel.
  10. Jan 5, 2018 #9
    Surely not, where would you look?
  11. Jan 5, 2018 #10


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    If the particle's energy is larger than the potential barrier's energy, then this might as well be a classical event.

    The particle has its own kinetic energy, and in a ballistic tunneling, this energy is conserved. It doesn't need any extra energy to go through the barrier, because this is not directly an event that consumes energy. When it exits on the other side, it has the same energy as before.

    This is why this is a quantum mechanical phenomenon.

  12. Jan 5, 2018 #11
    So are you saying a free electron, happily migrating through a metal and near a MIM structure, and with kinetic energy of 0.01234eV, has some probability of tunnelling through the MIM (which has say, a 2nm thick insulator with measured barrier heights (total) of say 1eV), and emerge with a kinetic energy of 0.01234eV in the other metal, where it is free to continue its unbound journey?
  13. Jan 5, 2018 #12


    Staff: Mentor

    Please explain what you mean by migrating through the metal? The tunneling effect speaks of nothing like that. It simply predicts the probability of where you will find the particle. It's just a weird quantum effect - no more than that - if you try and read more into it you will go down the gurgler. Simply accept QM as a theory about probabilities as described in the following and you never run into problems:

    Applying classical intuition to QM is fraught with danger.

    Remember what our patron saint (that's what Leon Lederman called him - couldn't resist) Feynman said in situations like this - recall the double slit - you say of course - he replies - same thing. As the article I linked to explains it all comes from the simple extension of probabilities to negative numbers (actually complex numbers - but we start simple) and how to make sense of such a silly thing. Its part of a more generalized view of probability called generalized probability models. All QM is, is the next most complex such model after ordinary probability theory. It allows so called pure states to continuously change to other pure states which ordinary probability does not allow - but of course in modelling physical systems as pure states is something that is really nice to have. That's the formal basis of QM - that's why you get these weird effects. What it means - now that is a whole different story. Athough not widely known people argue about what ordinary probability theory means as well:

    Since its just an extension of ordinary probability theory it of course is also argued about - but much more because its so counter intuitive and you are faced with - why would nature do such a 'silly' thing in the first place. Me - I just say nature is as nature is - I hold to a very minimal interpretation and don't worry about it. If you want to worry about it - go ahead - but virtually all who have, with very rare exceptions like Bell, have got nowhere.

    Last edited: Jan 5, 2018
  14. Jan 5, 2018 #13
    Hi Bill, are you saying there are no electrons in a metal near an insulator interface as described that could tunnel to the other side, or are you saying there are no electrons with 0.01234eV energy?
  15. Jan 5, 2018 #14
    Bill, let me be more direct and clear, there is too much wishy washy talk of electrons tunnelling when their energy is less than a MIM barrier(s) of say 0.2eV.

    Are people seriously believing that there are tunnelling electrons with kinetic energy of say 0.1eV???? or as I asked 0.01234eV?

    BTW thanks for the amusing link, a shame if people think that accepting everything is the way to go for teaching the next generation of physicists, but I can see how it reduces the cost of producing a technician.
    Last edited: Jan 5, 2018
  16. Jan 5, 2018 #15


    Staff: Mentor

    I am saying QM is a theory about probabilities - specifically probabilities of observations. Talking about whats going on such as tunneling through without specifying the observational context of such a statement is not what QM is about. You must understand what the theory says and use language appropriate to what it says. What do you mean by tunneling particles - describe exactly the observational context you are considering. The observational context of the quantum well where it 'tunnels' through the well is it gives the probability of finding the particle - some of the probability is outside the well. There is no 'tunneling' involved such as say a termite tunneling through some wood. Its just a name for a weird effect.

  17. Jan 5, 2018 #16
    Hi Bill, I think you are avoiding a question I put, even if it was asked with some shortcomings.

    I am amused by the QM etiquette you wish to impose, when all I asked for was a number followed by eV.

    Take almost any text or explanation tritely offered, people will talk about a barrier, an electron approaching said barrier, and the probability that it (as a wave function) will pass through that barrier even if the barrier is "higher" than the electrons kinetic energy.

    So I asked the question, if there is an electron approaching a barrier (and for that I proposed the metal side of a MIM structure), described as 0.2eV high, then if someone says the electron energy is less that the barrier potential, what is the actual ballpark electron energy. My guidance answer is that the electron has an energy, "actual" energy far greater than 0.2eV, try perhaps say 4eV (obviously dependent on the materials used).

    Are you seeing why I am critical of these silly textbook examples?

    Fact; there are never going to be any rational examples of an electron (a wave function) with a kinetic energy of 0.01234eV tunnelling through a known MIM structure, agree or disagree?

  18. Jan 5, 2018 #17


    Staff: Mentor

    And what @bhobba is trying to tell you is that there is no such number. The electrons do not have a kinetic energy during tunnelling, because you are not measuring their kinetic energy during tunnelling. If you don't explicitly measure a particular property of a quantum object, you cannot treat it as having that property. That's just how QM works.

    If you want to get more specific than that, then, as @bhobba said, you need to get more specific about exactly what you are going to measure and how you are going to measure it. Just saying "the electron tunnels through the barrier" won't cut it.
  19. Jan 5, 2018 #18
    I know the electron does not have kinetic energy in the gap if it is not real, obvious, that is not my point. People talk about the energy of an electron approaching a barrier, what do they mean by an electron's energy, if not its kinetic energy. They could be talking about its potential energy, its kinetic energy, or both, but almost always the textbook examples, and the efforts of people instructing others, use the simple scheme of saying "an electron with 0.1eV approaches a barrier of 0.2eV".......... and with less than certain probability emerges on the other side with the same energy.

    These examples are what I am calling out, but people here seem to want to give me a lecture on QM rather than saying the teaching is bad.

    Again I say, there is no such thing as an electron with sum energy (KE + PE) sensibly being described as being 0.1eV, tunnelling through a MIM structure made, for example of Ni/NiO/Ni.
  20. Jan 5, 2018 #19


    Staff: Mentor

    Yes - they do say things like that - but it suggests things that are not what is really happening.

    If you want to see a correct explanation of tunneling, including whats going on inside the barrier, using the least amount of ordinary language as possible so as not to suggest things that confuse, see page 110 of Ballentine - QM - A Modern approach. It explains things not normally talked about in less advanced texts such as the so called work function.

    Think of it this way. You have a barrier made of some material. In order classically to get to the other side it must jump over the barrier. But that barrier is quantum stuff as well. It interacts with the quantum stuff of the barrier in such a way it doesn't have to jump the barrier - but rather you need to treat the system as a whole, and when analysed that way you find the wave-function can be inside the barrier and even the other side. More technical details as I said can be found in the referenced textbook.

    Last edited: Jan 5, 2018
  21. Jan 5, 2018 #20


    Staff: Mentor

    Please give a specific reference--textbook or peer-reviewed paper. We can't discuss vague allusions. We need something concrete to base our discussion on.

    Then please find a specific one, instead of generalizing.
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