Saturday, September 26, 2009

Tunneling and STM

A few weeks ago, I gave a guest lecture (read: "I am at a conference that day, could you do it for me?") in a course entitled Unifying Concepts in Nanoscience. The topic was basic quantum mechanics (chapter 9 and a bit of 10 in Atkin's Physical Chemistry): particle in a box, etc.

These days, the first thing I do when preparing a lecture is to scour Molecular Workbench for useful animations, as I have discussed in a previous post. True to form MW did not disappoint, and I put together the following set of MW slides (note: you need to install MW first before clicking on it).

The screencast above shows how I used four of the slides to illustrate the concept of tunneling and and how it applies to STM.

Once again, I found animated simulations in general, and MW in particular, invaluable in bringing across complex concepts. And once again MW did all the hard work.

2012.09.01 UpdateI made a few more screencasts of parts of my lecture


Anonymous said...

Great blog! I am still have to explore it but this kinf of hints are very usefull for sure. Thanks!

Greetings from Brazil.


Jan Jensen said...


Thanks very much. That's great to hear.

Unknown said...

Hello Jan
I am Bassirou from Senegal (Africa) and I would like to say thank you for your work.
I am studying Physics in Seoul (South korea).

Jan Jensen said...


you're welcome. Glad to hear you like the blog.

Roysten said...

Nice, am giving a talk on how STM works next week, your blog has given me some good insights on getting some points across. Cheers!

Jan Jensen said...

Roysten - glad to hear it!

Unknown said...

Dear Sir,

Thank you very much for this work. I am a physics student and STM has never been so clearly explained to me before.

Keep up this great work.

Jan Jensen said...

Thanks, Vishnu. Of course most of the credit goes to Molecular Workbench.

Robert L. Ayers said...

Perhaps I am mistaken, but there appears to be an error in this animation during the part where it shows the time dependent solution (approx 33 seconds in).

If I understand the bar labels correctly, TE = Total Energy, PE = Potential Energy, and KE = Kinetic Energy. If this is the case, then TE should stay constant, while KE and PE vary inversely with respect to one another in a nice sinusoidal fashion.

In other words, PE should go up as KE goes down, and vice-versa. In this animation, they both go up and down at the same time, while the TE bar stays constant.

Jan Jensen said...

Robert, good question. I think the answer is that the TE and PE are negative numbers (notice the labels on the y-axis) and that the bar shows the magnitudes of these energies. Thus, a longer PE bar means a lower (more negative) value.

Anonymous said...

Thank you very much for great work.
I'm a chemistry student and taking physical chemistry course in U.S.
This video gave me clear understanding of tunneling.


Jan Jensen said...

Ryoko, very happy to hear it! Thank you.

Charles Xie said...

Jan, you are exactly right. The bars show the absolute values of KE, PE, and TE. The 1D time-dependent Schrodinger equation (TDSE) solver uses the fourth Runge-Kutta method and both occupancy and total energy are conserved.

This, however, isn't the case for the 2D TDSE, which uses the Crank-Nicolson method. The occupancy is strictly conserved, but the total energy isn't. The solver is unconditionally stable, which means any time step would not cause it to crash, but the TE fluctuates more when the time step gets larger.

A Runge-Kutta implementation for 2D would have been too slow, which is not good to achieve interactive simulations. The old saying is right: there is no free lunch. We the pathetic computational scientists often need to struggle between accuracy and speed. :)

Jan Jensen said...

Charles, I am just amazed that one can do this (quantum dynamics) at all in an interactive way.

By the way, one thing I missed when talking about tunneling was a way to change the barrier width and height in the 1D case.

Anonymous said...

Dear Sir,
I am material Science student,thank you so much for this help, it is clear now.
ich danke Ihnen fuer Ihre Hilfe(DE).

Jan Jensen said...

Bitte schön

Anonymous said...

I just love how scientists can finally explain to themselves how musical instruments in an ensemble correspond with one another, and how Tesla's resonant systems actually work! In more plain language, QUANTUM TUNNELLING IS SIMPLY HARMONIC RESONANCE!!! Thank you, scientists of the world.

Anonymous said...

Thanks for the video, it's very didactic!
Which is the software? It's very interesting, it's possible to download it? Thank you very much again!

Jan Jensen said...

Glad to hear you found the video useful. I simulations are done using Molecular Workbench. The links are in the blog post.