Quantum physics research...?

Pre-College Issues High School Life
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<p>So I was browsing the forums for a while earlier and I came upon this post:

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I got interested in quantum physics/quantum computing research in my sophomore year and have continued it through senior year. It ended up turning into a mathematical, experimental, and computer simulation analysis of more effective quantum computing techniques. I got involved because I'd done research in various fields since 6th grade and wanted to find something I liked to concentrate in throughout high school. Namely something I could continue working with in college. I hadn't taken any special science classes previously, just Honors Biology I think which doesn't even apply to this topic. All the mathematics and theory I needed to learn I got through a mentor I found and self-study. Again, I didn't have a university to work with. All three years of experimentation was conducted in the back of my school's physics lab although I did have to borrow equipment from the local community college (they surprised me with how much equipment they had). As long as you're proactive in finding mentors and teachers who are open to helping you, you can accomplish a lot. I've entered the science fairs every year State wins and one ISEF, Intel Semifinalist.</p>

<p>To address username, I seriously just went to the library said "ok, I like physics, what's the hardest thing in physics that looks interesting to me that I could work with?"...quantum physics! Three years later I haven't looked back.</p>

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<p>I am also a high school sophomore deeply interested in quantum physics ... though I have to say, up to this point, I've only been exposed to the basic conceptual stuff. I've also never taken a physics class (though I plan on taking Physics C next year) and am currently enrolled in precalc. </p>

<p>I'd like to pursue independent research on a quantum physics topic and go with it for the next couple years. Given my obviously inept background for this kind of pursuit, can anyone who has done independent research give me some tips on how I go about self-studying for a sufficient math and physics background? Where should I look for information on quantum physics (and its open questions) itself - the library, a professor, etc.?
Thanks.</p>

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<p>Well, you’re not even near the level of math that is required for quantum mechanics. Schrödinger’s equation, for example, is a partial differential equation. You’d basically need to teach yourself single variable calculus, multivariable calculus, linear algebra, ordinary differential equations, partial differential equations, and probably a bit of fourier analysis. In addition to all of the math just to get caught up, you’d need to also learn up to quantum mechanics in physics. That’d require the Physics C curriculum, plus a sophomore level classical mechanics/electromagnetism course (it’s much more involved than the Physics C curriculum). After all of that, you’d be able to get started with quantum mechanics. I wouldn’t recommend even attempting to look for an open problem in quantum physics yet until you’d get up to the level thats required.</p>