Say I study a maths B.sc. with a physics minor. Say I grab quantum mechanics. Would I be able to write a paper on mathematical properties of quantum mechanics or would I need to actually study a full physics B.sc. for that?
Say I study a maths B.sc. with a physics minor. Say I grab quantum mechanics. Would I be able to write a paper on mathematical properties of quantum mechanics or would I need to actually study a full physics B.sc. for that?
It's tough for us to guess at your capabilities.
While physics isn't entirely serial in it's development it is fairly hierarchical.
Quantum mechanics is very much built on classical mechanics. If you don't know what the Hamiltonian is from classical mechanics QM is going to be very mysterious even if you are able to complete the problems.
In general it's a bad idea to try and shortchange your studies and there is no reason to. With the math you will have you'll be able to understand CM without any difficulty.
Do you have an scholastic advisor of some sort? It sounds to me as if you need someone you can trust and can discuss these things with in person in an actual conversation.
Well my train of thoughts is...I want to use my mathematics for physics and I'm thinking that my best shot is in quantum mechanics, due to its fairly 'recent' discovery...Or am I far off? I'm not a master's or a PhD student but I want to be one day and I'm just throwing some ideas out there for feedback.
well as Deveno said earlier you should plan on doing what you enjoy doing. QM has been around 100 yrs or so now so it's hardly recent.
Part of the idea of learning a subject hierarchically is that you get a much better idea of where you want to head as you learn it.
This is wonderful and I think will help you gather your thoughts.
Gerard't Hooft is one of the more important living physicists. He shared the Nobel Prize in 1999.
What you linked is basically a list of a B.sc. physics degree. As I said, I don't intend on studying a physics B.sc. but I would like to contribute to the mathematics of quantum mechanics. Is this impossible without first taking a physics B.sc.?
Sure it is possible for you as a pure mathematician to contribute to the mathematics of quantum mechanics or quantum field theory without having the physics degree. There are various ways you could do this, innovative ways of performing approximation calculations comes to mind. New methods of dealing with non-linear differential equations would certainly be welcome. You certainly wouldn't need a physics degree for any of that, though I suspect that by the time you were done you would have a level of understand of the topic at hand equivalent to one or better.
Here is an example of innovative pure mathematics having a startling application to particle physics which should fall under your umbrella of quantum mechanics. Note that the authors are mathematical physicists. I don't believe they were working on the problem from a purely mathematical point of view, but nevertheless.