# Computational project in quantum physics

## Main Question or Discussion Point

The professor of my undergrad quantum course said that I could get some extra credit if I did some sort of outside project and presented it to the class (for example, for my E&M Professor I built a Tesla Coil). Since it will be somewhat difficult to do something physical/hands on for quantum physics, I am going to do some sort of computational exercise. What, though, I have no idea...

The first thing that comes to mind is writing a program that models finite square wells or potential barriers based on boundary conditions provided at input. For example, I could allow for user input so it will evaluate the probability that the particle will be located at a given mouse click.

While this would be challenging, I would like to do something a little more...original. You know? I am reading some papers on quantum and atomic and nuclear physics to get some ideas but so far I just don't know. Any thoughts? Thanks!

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ZapperZ
Staff Emeritus
2018 Award
When you try to do something "computational", it is always nicer to solve something that can't be solved analytically. The finite square well potential can be solve rather "analytically", even if you end up with some transcendental equation.

You didn't say what kind of computational method background that you have. Have you solved differential equations before computationally using techniques such and Runga-Kutta? If you have, then maybe solving for something such as an image charge barrier potential problem might be fun (and useful), such as finding the probability of tunneling for a particle in such a barrier potential. The application for this is in the solving of field-emission equation (i.e. Fowler-Nordheim model), the thermionic emission (Richardson-Dushman model), and even the Schottky-effect in photoemission.

Zz.

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The professor of my undergrad quantum course said that I could get some extra credit if I did some sort of outside project and presented it to the class (for example, for my E&M Professor I built a Tesla Coil). Since it will be somewhat difficult to do something physical/hands on for quantum physics, I am going to do some sort of computational exercise. What, though, I have no idea...

The first thing that comes to mind is writing a program that models finite square wells or potential barriers based on boundary conditions provided at input. For example, I could allow for user input so it will evaluate the probability that the particle will be located at a given mouse click.

While this would be challenging, I would like to do something a little more...original. You know? I am reading some papers on quantum and atomic and nuclear physics to get some ideas but so far I just don't know. Any thoughts? Thanks!
Don't know if you could be interested, in an old article of Scientific American (June 1994) called "The classical Limit of an Atom" it's written that a a wavepacket made by the superposition of many atomic levels with high quantum number n can disperse and clump periodically along an almost classical orbit around the atom (at very high distances from the nucleus). It's said the treatise is semiclassical; maybe you can make a program which simulate such a behaviour.

When you try to do something "computational", it is always nicer to solve something that can't be solved analytically. The finite square well potential can be solve rather "analytically", even if you end up with some transcendental equation.

You didn't say what kind of computational method background that you have. Have you solved differential equations before computationally using techniques such and Runga-Kutta? If you have, then maybe solving for something such as an image charge barrier potential problem might be fun (and useful), such as finding the probability of tunneling for a particle in such a barrier potential. The application for this is in the solving of field-emission equation (i.e. Fowler-Nordheim model), the thermionic emission (Richardson-Dushman model), and even the Schottky-effect in photoemission.

Zz.
ZapperZ - Thanks for the thoughtful reply! I have had a course in Computational Physics and am semi-familiar with the Runga-Kutta method of solving differential equations. I would use IDL to program this, as I am most familiar with it. The tunneling idea is great, I might just do that..but what literature should I investigate to understand some of the possible applications better (those you listed)? I will look through the books on quantum mechanics in the physics library later tonight, but I figure the best data will be through publications. Any suggestions?

Don't know if you could be interested, in an old article of Scientific American (June 1994) called "The classical Limit of an Atom" it's written that a a wavepacket made by the superposition of many atomic levels with high quantum number n can disperse and clump periodically along an almost classical orbit around the atom (at very high distances from the nucleus). It's said the treatise is semiclassical; maybe you can make a program which simulate such a behaviour.
lightarrow - That sounds interesting! Do you know where I can find some more information on that? There is a stack of Scientific Americans in the Physics library, I will also check those out later tonight for that issue (couldn't find much on google).

ZapperZ
Staff Emeritus
2018 Award
ZapperZ - Thanks for the thoughtful reply! I have had a course in Computational Physics and am semi-familiar with the Runga-Kutta method of solving differential equations. I would use IDL to program this, as I am most familiar with it. The tunneling idea is great, I might just do that..but what literature should I investigate to understand some of the possible applications better (those you listed)? I will look through the books on quantum mechanics in the physics library later tonight, but I figure the best data will be through publications. Any suggestions?
There is a classic text by Modinos on Electron Emission. That's what I use. However, this book is out of print, and I'm sitting on the only library copy available here. :)

I think if you have access to various journals at school, then you might find a good source somewhere. If you can't find any, write back. I'll check what I have when I get to work tomorrow and give you a list of papers.

Zz.

lightarrow - That sounds interesting! Do you know where I can find some more information on that? There is a stack of Scientific Americans in the Physics library, I will also check those out later tonight for that issue (couldn't find much on google).
Regards.
lightarrow.