Undergraduate Research: Emailing Profs

This autumn, I will be enrolled as a freshmen for my first semester at a large, public research university. Despite still being in high school, I feel that I am almost as prepared as ever to make contrabutions to mathematics and physics (Specificially, my main interest is the application of symplectic geometry to quantum mechanics. I have other interests such as quantum computing, ergodic theory, Bohmian mechanics, and mathematical music theory.)

However, I know very little about, and admittingly frightened of the prospect of, the research and publication process. Also, I probably need some (or a lot of) help in the form of collaboration. Therefore, I am planning to email some of my prospective professors/research advisors/collaboraters whose research fields have sufficient overlap with my interests.

Since this would be my first time interacting with these very important people, I would like to make a good first impression. I hope I don't screw up.