Source of energy for quantum tunneling of a particle

[SameerTahir]

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?

 

[nomadreid]

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.

 

[jtbell]

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.

 

[Demystifier]

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?

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.

 

[Demystifier]

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.

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.

 

[PhilQ]

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.

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).

 

[vanhees71]

Could you refer to original papers about this experimental findings. I don't understand what you mean.

 

[PhilQ]

Could you refer to original papers about this experimental findings. I don't understand what you mean.

Sure, here is one reference I have on hand;

Focusing of tunneling electron in a magnetic field

• Haruo Tanakaa, ,
• Hiroshi Itoa,
• Toshiaki Iitakab,
• Yoshihiko Ohstukia

• 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
Abstract
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.

 

[PhilQ]

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.

Surely not, where would you look?

 

[ZapperZ]

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?

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.

Zz.

 

[PhilQ]

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.

Zz.

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?

 

[bhobba]

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?

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:
https://www.scottaaronson.com/democritus/lec9.html

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:
http://math.ucr.edu/home/baez/bayes.html

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.

Thanks
Bill

 

[PhilQ]

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:
https://www.scottaaronson.com/democritus/lec9.html

Applying classical intuition to QM is fraught with danger.

Thanks
Bill

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?

 

[PhilQ]

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.

 

[bhobba]

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?

I am saying QM is a theory about probabilities - specifically probabilities of observations. Talking about what's 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.

Thanks
Bill

 

[PhilQ]

I am saying QM is a theory about probabilities - specifically probabilities of observations. Talking about what's 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.

Thanks
Bill

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?

PhilQ

 

[PeterDonis]

all I asked for was a number followed by eV.

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.

 

[PhilQ]

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. If you're not familiar enough with actual experiments and results to be able to get that specific, then the response should be obvious: fix that.

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.

 

[bhobba]

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

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 what's 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.

Thanks
Bill

 

[PeterDonis]

People talk

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.

These examples are what I am calling out

Then please find a specific one, instead of generalizing.

 

[bhobba]

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.

If your intent is to suggest the usual teaching of QM is bad (well at least not as good as it should or could be) - I am with you. But Rome was not built in a day - you need the concepts built up gradually - some of which you have to forget and learn something different. See Myths of QM:
https://arxiv.org/abs/quant-ph/0609163

Ballentine is an advanced textbook and nobody in their right mind would recommend it as first exposure. You need to build up to it - but it gets the concepts right. So in your QM journey simply note some things that are not clear to you and keep them in the memory bank so to speak until you get to Ballentine, or similar advanced text.

Thanks
Bill

 

[bhobba]

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.

The energy it has in the situation you are considering. Say you have an electron created with known energy approaching the barrier - that energy is the energy it was created with in the setup you are considering. Now between the point in time you knew its energy - by some form of measurement, hypothesis, or whatever, and it interacting with the barrier we have no idea of its energy. QM say nothing about unobserved things - its a theory about observations - when not observed it says nothing. It has a complex interaction with the barrier - more detail is explained in the reference I gave - Ballentine - and from that interaction it has a certain probability of being in the barrier or on the other side - even though the energy is not enough, when it was measured or somehow inferred, to jump the barrier.

Thanks
Bill

 

[bhobba]

Please give a specific reference--textbook or peer-reviewed paper. We can't discuss vague allusions.

He did - but I don't have access to the paper so can't read it to comment.

All I can do is elucidate general principles and give a reference to a standard textbook.

If he can actually post the paper or provide an online source then it will be much easier to sort out.

Thanks
Bill

 

[PhilQ]

Perhaps readers might refer to the posted reference as to tunnelling electrons curling in a magnetic field. Noted by the researchers were electrons

The energy it has in the situation you are considering. Say you have an electron created with known energy approaching the barrier - that energy is the energy it was created with in the setup you are considering. Now between point in time you knew its energy - by some form of measurement, hypothesis, or whatever, and it interacting with the barrier we have no idea of its energy. QM say nothing about unobserved things - its a theory about observations - when not observed it says nothing. It has a complex interaction with the barrier - more detail is explained in the reference I gave - Ballentine - and from that interaction it has a certain probability of being in the barrier or on the other side - even though the energy is not enough, when it was measured or somehow inferred, to jump the barrier.

Thanks
Bill

Hi Bill,

We note the paper I cited above about the experiment to determine if a tunnelling electron is subject to a magnetic field, they proved that it was, similarly electrostatics are part of the mix. The thing is that if we allow on one hand loose ideas of electrons approaching a barrier... with 0.1eV, and at the same time ponder the curl of a magnetic field acting upon tunnelling electrons (or shall I say the way they put it, bend as though it were a non tunnelling electron), some might expect that a 1T magnetic field might curl a tunnelling electron with a radius of less than say 10nm, agree?

However the reality is that in any likely structure the electron curl radius is going to be many um, as the virtual velocity of the tunnelling electron is going to be some millions m/s, agree, or not?

 

[bhobba]

as the virtual velocity of the tunnelling electron is going to be a million m/s, agree, or not?

Virtual velocity of the tunneling electron- what's that?

The whole experiment needs to be analysed quantum mechanically to sort it out. I can't do that unless the paper is posted - and even then I am not really into experimental stuff - but we have those that are.

However I will also have to tell you we have many professors that post here and quite a few papers that get discussed would not be passed by them as a referee.

Thanks
Bill

 

[PeterDonis]

you have done nothing here I would ban you for.

For info, in PhilQ's other thread I asked him for a reference, since he was posting the same claims as he is making here and provided no specific example, despite repeated requests in this thread. I did not say he would be banned from PF, only thread banned. However, another moderator has now given him a warning which resulted in a temporary ban from all posting on PF.

 

[ZapperZ]

I know that the "intruder" to this thread is on a temporary "hiatus", but I do not understand the brouhaha here. He/she seems fixated with this "small" energy scale of sub-eV, and somehow thinks that this might prevent any form of tunneling.

The problem here is that the "scenario" isn't very clear, based on what he/she is arguing here, and in another thread related to this. This is why we need to go back to the simplest, intro-QM level, and see where the issue lies. In the simplest case of free particles encountering a square barrier, this should be very clear because ALL intro-QM students had to deal with it, so why can't we start there?

See Pg. 11 of this document. The parameters and symbols used are explained in the text. The transmission coefficient, which tells you the probability of tunneling, depends on the factor of

exp{-2βx}

where β = {√2m(V-E)}/ħ.

This means that, other than when the exponent is negatively infinite, there is a non-zero probability of tunneling.

His/her fixation on the energy scale is puzzling. I used to perform SIN (superconductor-insulator-normal metal) tunneling experiments in which the energy scales are in the MILLI-eV, i.e. the KE of the electrons passing through the energy gap is in the milli-electronvolt scale (look at the energy gap size for a typical conventional superconductor). So the energy scale here does NOT prevent any form of tunneling, especially in NIN (normal metal-insulator-normal metal) junction where there are no gaps in the density of states around the Fermi energy.

Zz.

 

[bhobba]

You could be right - I simply do not understand his concern. He speaks of 'virtual paths' and other claims in the paper he has mentioned - but it is not generally viewable so what his context is can't be checked. If the paper can be seen in its totality then I feel confident what he is concerned about can be better understood. Right now I don't get it, nor why he got so upset.

Of course the size of he barrier makes no difference - why anyone would think so beats me.

Thanks
Bill