Wednesday, May 4, 2011


I'm going to discuss yet another strange prediction of quantum mechanics - quantum tunneling. This effect allows scientists to image very tiny objects (atom sized objects) via a device called a scanning tunneling microscope (like the image to the left). That image is several atoms arranged in a ring, those bumps you see are the atoms! I direct you to Nano Nook for another example image.

So what is quantum tunneling? Well, think back to the potential that goes into Schrodinger's equation. Speciffically, I want you to consider a potential that looks like this.

You can visualize this like two hills that are sitting next to each other. Image you're sitting in the valley on the left, but you haven't eaten all day an you're exhausted. All your friends are waiting in the valley to the right, but you can't get there! You don't have enough energy! Well, this is the classical physics way of looking at things - no matter how hard you try, you don't have enough energy to make it up and over the hill.  Well, quantum mechanics says, you don't have to! Since your wave function extends in space, a small part of it overlaps with the other valley! What does this mean? There's a finite chance that you could be in the hill to the right! This is what quantum tunneling says, and this effect has been measured and is currently used a device called the scanning tunneling microscope (as well as MANY MANY other technologies.) Here's a gif I stole from wikipedia that shows this happening... sadly I didn't have time to make a simulation of my own.

Here you see a quantum particle penetrating a wall.

So how does the scanning tunneling microscope work? It's actually reasonably complicated, but the basic principle is as follows. A tungsten tip is held above the surface that you wish to image. There is nothing but vacuum between the tip and the surface, so normally, there's nothing to allows the electrons to flow to the surface. Fortunately for us, there's a finite probability that the electrons will "tunnel" to the surface, and this effect allows us to image the surface to extreme detail. Pretty cool, huh?


  1. Very cool, and sort of mind blowing. I'm probably asking a stupid question, but does this connect to string theory at all? It seems like it has some parallels.

  2. Cool indeed. I read about this in my Electronic Properties of Materials explained it better ;)

  3. Jen, it does because String Theory is a quantum mechanical theory, but it doesn't need string theory, and is perfectly well handled by current quantum theory.

    I want to be clear though, when I say tunneling, I'm not talking about a wormhole or something like that. I'm merely talking about the fact that quantum mechanics says a particle has a probability of being almost anywhere, and in tunneling situations, this probability is great enough that it happens frequently.

    Wormholes would be distinctly quantum gravity phenomena - a VERY challenging subject. This would be a string theory connection. Who knows? Maybe that's why quantum tunneling happens. Only time will tell. Thanks for the great question!

    Also, thanks Sean, I try!

  4. the explanation is good.Can you explain distance dependent(between tip and surface) variation of image quality using a mathematical expression which contain lenth of box(particle in a 3D).

  5. venki, I definitely wouldn't call myself an expert on STM's. I don't know a good answer to your question.