Undergraduate Senior Physics Research Topic (Theory)

[matheophys]

Hello all,

This is most likely a question for those who have experience/knowledge of theoretical/mathematical physics at the graduate level and can provide recommendations following my criteria.

Here is some background about me:

I am a senior majoring in math and physics at a small university and am required to choose a topic to perform research on for my senior year. My university does not offer any graduate programs in physics, so I am essentially required to come up with a topic by myself as my professors which do perform research are mainly experimentalists and I'm not to interested in their research.

As mentioned in the topic, I am particularly interested in a theory based project as opposed to experiment since 1) beneficial experimental projects here are simply not attainable for financial reasons and 2) I am interested in pursuing a career in theoretical/mathematical physics post undergrad.

My specific goals for this project are simple. I do not expect to do cutting edge, original theoretical research. I would simply like to pick a topic which is well established and would allow me to learn a substantial amount of new physics and mathematics in preparation for graduate school. In particular, I would like to pick a mathematical/theoretical topic which, once an adequate amount of the theory has been learned on my part, has a substantially difficult problem/calculation accessible to an undergraduate I could then apply what I've learned too. Once having done this I would then compare my results with what has been established or a computer simulation.

At the moment, my interests in potential topics include particle physics (Griffiths Book) where I could calculate the lifetime of a particle- although I'm not sold on this problem- or general relativity ( Shutz, hartle, Moore, Thorne etc.) of which i haven't a clue of a potential target problem/calculation.

Finally, I should mention i am quite competent in the following areas at the standard undergraduate level i would assume: calculus(multi variable, vector etc.), linear algebra, differential equations, applied multi variable calculus in statistics, beginner formal maths (number theory, real analysis,geometry), thermodynamics (baierlein level), E&M (Griffiths), classical mechanics (Taylor), quantum mechanics(david mcintyre),modern/atomic/nuclear physics (Townsend/Riesnick).

I have a whole year to complete this project, so it can be fairly large,rigorous,challenging and demanding.

Thank you for any assistance in this matter!

 

[Dr. Courtney]

Most theory projects accessible to an undergrad are going to be computationally intensive. Are you a good programmer? Have you taken a good numerical analysis course, and can you really apply what you have learned?

I think your best bets may be solving some (non-relativistic) quantum mechanics problems with numerical muscle or possibly investigating (computationally) some classical systems that are chaotic or transitioning to chaotic.

 

[Vanadium 50]

If you want to work in an area where none of the faculty are active in, how do you expect to get help and guidance?

 

[Dr. Courtney]

If you want to work in an area where none of the faculty are active in, how do you expect to get help and guidance?

This is a good point, but there are a few options for students to find project mentors in areas where their school does not have faculty expertise.

We work with a few students every year who email us and express an interest in doing a project in an area in which we have expertise (blast, ballistics, chaos, acoustics, atomic physics). The admins in their local departments have always approved our mentoring of their projects, because we offer opportunities otherwise unavailable. Remote collaborations have become commonplace and can be productive if the student has a good work ethic.

The NSF sponsored REU programs also require that REU sites offer a certain number of research opportunities to students outside of their home institutions.

There are also plenty of opportunities in government and industry labs, but these positions require a pretty strong application to get.

I see lots of benefit in working with local faculty, and a student should usually explore all of the local options first. But there are options beyond that if needed. I recall as an undergrad feeling like I had won the lottery when the only experimental atomic physicist at LSU invited me to work in his lab. But I needed to get more creative a year later when he accepted a position at another institution.

 

[matheophys]

Unfortunately, I had not decided this path prior to my choice of university. With no help or guidance available in my particular area of interest, I hadn't really expected any but I would assume there would be a way to make it without any. Obviously I am quite naive in my approach. However I have applied to numerous REU Experiences this summer. I had never thought about collaboration with faculty at a local university, but it is something I will most definitely look into.

 

[Dr. Courtney]

Unfortunately, I had not decided this path prior to my choice of university. With no help or guidance available in my particular area of interest, I hadn't really expected any but I would assume there would be a way to make it without any. Obviously I am quite naive in my approach. However I have applied to numerous REU Experiences this summer. I had never thought about collaboration with faculty at a local university, but it is something I will most definitely look into.

Put a good resume or CV together and send some emails. Even better, if you can, make the rounds in person, hand them your CV or resume, and communicate how hard you will work.

 

[JPBenowitz]

Take a look at Molecular Dynamics Simulation research. It's a relatively new and exponentially growing field. If you are interested and have access to a linux machine you can start setting up simulations and writing scripts to analyze the data rather quickly.