Exploring Quantum Tunneling: Origins, Experiments, and Interpretations

[Prologue]

I'm trying to wrap my brain around the notion of tunneling and am hoping somebody could be of assistance.

I'm wondering about the history of the idea, why was the notion of quantum tunneling first created? (What prompted the idea?)

Also, I'd like to find experiments that have shown that quantum tunneling is the appropriate way to interpret what is happening rather than an intuitive approach that I keep hanging on to and can't shake. (I'm thinking that it could be based on various energies for the particles, like that of a Boltzmann distribution for gas particles. Then only the higher energy particles have enough energy to get through, etc.) So evidence that shows the correct path would be greatly appreciated.

 

[Ken G]

(I'm thinking that it could be based on various energies for the particles, like that of a Boltzmann distribution for gas particles. Then only the higher energy particles have enough energy to get through, etc.)

That isn't it, because you can prepare particles in very precise energy states and you'll still get the effect. It sounds like what bothers you is that the particles don't have enough energy, so you want to imagine a few particles that do, but remember, what we mean by "have enough energy" can be interpreted in two ways. Classically, we say the particle has to have enough energy at all times, so cannot cross a "forbidden" region, but quantum mechanically, there is an uncertainty relation that says we are allowed to not conserve energy for short enough times, but at the end of the day the energy does have to be conserved. So this means the particle cannot linger in regions where it would not have enough energy, but it can make short forays through such regions. If at the place where the particle ultimately ends up after tunneling, it does have enough energy to be allowed to be there, then you can get tunneling without violating conservation of energy.

Even in forbidden regions, you can also find the particle, because the act of localizing the particle in the forbidden region will require using enough energy in the detection that it can explain how the particle got enough energy to be there! So the bottom line is, in quantum mechanics, the energies only have to work out in the end, after you include everything that happened including the detection itself.

So evidence that shows the correct path would be greatly appreciated.

I don't know much about the state of the observations, but you could google Josephson junctions to see a macroscopic example of the tunneling phenomenon in action.

 

[Prologue]

Thanks Ken. To me it seems that the jumping of electrons from one side to the other could be explained by collective well-timed collisions in the material. Just like water evaporating from our skin, the molecules themselves don't have the energy to just fly off. But due to a series of well-timed collisions one molecule can manage to escape (and doesn't come crashing back, leaving the others cooler). That is not tunneling, that is a macroscopic effect explained to me by random fluctuations in the molecules velocity due to collisions. However, when tunneling is introduced it is treated as one isolated particle so there would be no opportunity for it to be influenced from 'outside'. My big question is, how do we know for sure that this happens to single particles not influenced by outside things?

I'm checking out SQUIDS now, they are very interesting.

 

[Ken G]

My big question is, how do we know for sure that this happens to single particles not influenced by outside things?

The simple answer is, because quantum mechanics describes it that way, and quantum mechanics works great. But I know that you would rather have a physical example that is more concrete than a whole theory, so I would point to the NH3 molecule. IIRC, the 3 Hs make a triangle, and the N has to be on one side or the other of that plane, but by symmetry it is equally happy on either side. So the 3 Hs form something like a wall that the N does not have the energy to breach, but nevertheless the NH3 molecule emits a spectrum consistent with that N nucleus oscillating back and forth across that wall. The explanation is tunneling, and note there we do not have anything else happening that could bump up the energy of a new Ns-- they are all doing it, in isolation.

 

[ZapperZ]

Thanks Ken. To me it seems that the jumping of electrons from one side to the other could be explained by collective well-timed collisions in the material.

No you can't. That's nothing more than simple Drude model of conductivity.

If you look at, for example, the current versus voltage characteristics of tunneling current versus ohmic current in a superconductor-insulator-normal junction (i.e. your "electrons collisions"), you'll see the the characteristic is VERY different. The ohmic characteristics gives you the Ohm's law relationship, whereas the tunneling characteristics has a region where there's NO current whatsoever due to the energy gap in the density of states, something which a simple, normal transport would not be able to detect.

The same can be said about Josephson junction where supercurrent tunnel through the barrier. You get a huge current at zero bias, something that isn't expected with normal conductance.

So yes, they ARE different!

Zz.

 

[Prologue]

I really appreciate the replies but where can I read about this stuff? I would really like to see an introduction that involves a thorough explanation including clear arguments in math if possible. Where is this topic discussed, and which books are best for clarity (I appreciate the style of griffiths or similar)?

 

[ice109]

the clear argument is solving the shrodinger equation for a finite potential barrier which is treated in any introductory quantum book. i'll type it up when i get home.

 

[ZapperZ]

E.L. Wolf has a book that's almost a classic for tunneling spectroscopy (I used it for my graduate work). It's called "Principle of electron tunneling spectroscopy". I claim a direct "pedigree" from him since my graduate advisor was his student.

Zz.

 

[jtbell]

Many intro QM textbooks discuss how to solve the Schrödinger equation for the basic idealized tunnelling setup. Unfortunately, while setting up the solution is fairly simple, actually grinding out the transmission and reflection probabilities, and the complete wave function, takes a lot of algebra. Michael Morrison's "Understanding Quantum Physics" has most of the gory details in section 8.6 (Tunnelling for Fun and Profit).