Quantum Tunneling

Ok, I understand the mathematics of the phenomenon of quantum tunneling pretty well, considering I just finished my introductory quantum mechanics course. I can pretty much do all the math and calculate the probabilities that something will tunnel through a barrier.

So, why does quantum tunneling happen? I don’t know if I just missed something in my class, or if its one of those things that we observe but can’t explain. Any ideas?


“Tunnelling” gives a false impression of what’s going on here. It’s not that the particle is definitely on one side of a barrier, tunnels though then is definitely on the other side.

Subatomic particles are only probably in a given exact location. If they are close enough to a barrier there is a chance they are actually on the other side of that barrier sometimes. That’s the “tunnelling”.

Can’t a non-subatomic particle like a missle “tunnel” through a brick wall?

Even if it could be done it would take something like ten thousand years, IIRC.

I think it would be more like hundreds of times longer than the age of the universe.

This abstract http://www.aip.org/enews/physnews/1998/split/pnu357-1.htm
implies that the Tunnelling effect is more than an artifact of Schrodinger’s wave equation. In other words the subatomic particles probably can cross barriers for which they do not posess the energy to penetrate with the probability of this occuring being inversely proportional to the thickness of the barrier, and the size/frequency of the particle/wave in question. Stated simply the higher the frequency, or smaller the particle, and the thinner the barrier the more likely this is to occur. Indeed, the above article alludes to possible practical implications for the use of this phenominum with regard to mircroprocessor technology.

You may also wish to consider the questions and answers available here http://www.physicsforums.com/archive/f-62 .

I think it could happen instantly, but it’s almost impossibly unlikely to happen.

Sometimes this is as close to understanding as we get - obviously the true answer to ‘why’ is ‘it seems that’s just how the universe is.’

However, there can be analogies that help you visualise it, and help you have some intuition about it. I haven’t heard one explaining this… how about comparing it to spontaneous creation? It can ‘borrow’ some energy just long enough to get through the wall. Or imagine the probabilty distribution as a water balloon - it overflows the sides but only so far. OK, those suck. Anyone else?

I don’t have time to look this up now, but I could look at my notes later - I don’t think I have any calculations of the probability but I do have some phenomenological explanations. There are a few chemical reactions that are thought to take place by quantum tunneling, through space, without requiring the molecules to physically collide. They involve proton or hydride transfer, so the mass of the tunneling particle is very small, thus making tunneling much more likely. Usually the site to which transfer occurs is ‘guarded’ by large, interfering groups to prevent the transfer from occuring in the usual way but which make transfer by tunneling possible.

There is also a probability that they are in the barrier. That probability decays exponentially inside the barrier. But why is there a probability that the particle is in the barrier, or even on the other side? I suspect the answer is as Shade says, and we don’t know and can only calculate it.

That said, I was thinking of an analogy to a tennis ball hitting a wall. When it hits the wall, it deposits some of its energy into the wall. If that energy is high enough, then the ball ends up on the other side none the worse for the wear. If its not high enough, it stays on the original side of the barrier with all of its energy back. I thought this because when we are describing the ball inside the barrier, it has an exponential decay whose rate of decay is related to the energy contained in the ball when it hits the wall. Does this make any sense at all?

The fundamental problem with quantum mechanics is that it only makes sense as a mathematical theory. As soon as you try to translate it into normal language, everything just kinda falls apart. That’s why you need to avoid analogies with macroscopic objects: quantum objects are not like them, and comparisons can really only confuse you.

There’s nothing mysterious about tunneling with respect to wave phenomena. Both light waves and water waves can display frustrated total internal reflection which can be considered exactly equivalent to the behavior of the quantum mechanical wavefunction.

The problem is that the wave function isn’t real and represents the probability of finding a particle in an energetically forbidden region. This is where the wicket gets sticky and intuition goes out the window. Particles (in the classical sense) shouldn’t be able to do this. And this is an example of why Feynmann said that no one understands Quantum Mechanics.

From what I understand, it’s that a particle’s wavefunction never goes to zero as distance increases, it just becomes vanishingly small. But if you happen to look, you might be able to find that particle there because your act of observing (which usually involves bouncing photons at the particle) could give it just enough energy to exist there. Or something.

Yeesh. No wonder Einstein hated QM, too.

I’m not sure what kind of a “why” explanation you’re looking for. Physics is ultimately about describing the world around us. So the reason tunnelling can happen is “because of quantum mechanics”.

Think about a different question: why do planets have elliptical orbits? Answer: because gravity is an inverse-square-law force. But why is gravity an inverse-square-law force? Answer: because mass curves spacetime. But why does mass curve spacetime?

Do you see my point? Physics is really not about giving “why” explanations. Newton’s law of gravity “explains” why orbits are elliptical, but it doesn’t “explain” gravity, it just describes it. Same for General Relativity: gravity is described, not explained by curved spacetime. To the question “why is there gravity?” we can ultimately respond only “because there is”.

So why do small particles tunnel? They just do. QM describes how it happens (or, at least, how likely it is to happen).

I see your point FriendRob. But while trying to mathematically describe what happens, aren’t we also at the same time trying to discover why a particular phenomenon happens? Wasn’t trying to explain why the photoelectric effect happened what jumpstarted research into quantum physics?

I’ve always thought that science in general was supposed to describe what and why something happens. I do realize that we can’t always explain why something happens and have to say “because it does.” But that shouldn’t stop us from continuing to try and explain why something happens.

I would make a stronger statement than that, even. Frustrated total internal reflection is not just exactly equivalent to quantum tunnelling. It is an example of quantum tunneling. The only difference is that we’re much more used to talking about light as a wave than we are to talking about electrons as a wave.

The key point to tunneling is that when a wave (of any sort, classical or quantum) hits a potential barrier, it goes from being sinusoidal in character to being exponential, specifically, an exponential decay. Now, a sinusoidal wave can easily propogate as far as you like, without diminution, but an exponential “wave” is diminished quickly. Most of the wave will, at some point in the barrier, be reflected back out, but some of it will make it to the other side of the barrier. Once the wave reaches the other side of the barrier, where sinusoidal oscillations are again allowed, the continuity of the wavefunction guarantees that there will then be a sinusoidal wave on the other side of the barrier, at a lower amplitude. If we translate this back into terms of particles, what we’ll see is that most particles will be reflected off the barrier, but a few of them tunneled through to the other side and then kept on going.

Note, again, that this works on any level, for classical waves as well as quantum ones. Classical wave dynamics does, indeed, provide strong analogies to quantum mechanical behaviour. The only thing which makes quantum behaviour seem different than classical is the fact that, at a quantum level, everything is a wave. Quantum waves are not like classical particles, but they are like classical waves.