Undergraduate level research topic in physics

[manimaran1605]

I am a Final year (3rd year) student studying BSc Physics in India. My undergraduate course is getting completed in one month. As I want to pursue my career in field of physics, I like to do a project especially a theoretical project (kind of writing a junior level thesis) before joining Postgraduate course. I will be having atleast two month free time. I am planning to approach professors in universities on my location, for that i have to be sure what i am proposed to do (project i am willing to do). Honestly to say I have no idea what to do. But I already done a reading project in Quantum mechanics for a month and presently i am learning Complex analysis(mathematical physics).
I have interest in these topics (1) Quantum mechanics (Matrix mechanics, Hamiltonian)
(2) Mathematical physics (Matrix theory (upto eigenvalues, eigenvectors, some linear algebra), harmonic analysis (upto Fourier transforms, Fourier series, etc)
Please Suggest me some Undergraduate level Research project topics that I can do and I acquired some knowledge through my undergraduate course on these topics i mentioned above.

Thank you in Advance​

 

[fsujoseph]

I am only in year 1 of my undergraduate degree, but as long as you know some maths you can contribute to really any project by doing the grunt work.