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I am a first year PhD math student, and I am wondering if I should study quantum mechanics even though I don't have an undergrad background in physics.

I posted this question in physics stackexchange, but there doesn't seem to be many people interested in it there. In addition, I want to hear those who are just like me, math students who want to study theoretical physics and have difficulties with physics background (not to say also math background).

I actually studied computer science in undergrad. I switched to graduate math because I wanted to study quantum computing / information and in the long term to be involved more in quantum mechanics.

In the first two years of undergrad, I actually took general physics (physics for non-physicist students) courses: mechanics, thermodynamics, electromagnetics, modern physics. However, now 5 years later, I forgot most, not to say all, of them. Those courses obviously did not cover Lagrangian or Hamiltonian things, and taught very little (very insignificantly) about the Maxwell equations and the Schrodinger equation.

Now, I also don't know anything about partial differential equations, but I could take a graduate "Methods of Applied Maths" course in parallel with quantum mechanics.

Do I need to prepare more physics and mathematics before taking graduate quantum mechanics? What books should I use to prepare for those topics?

Have any mathematicians taken a quantum mechanics qualifying exam to get a multi-discpline degree?

Your experience and advice will definitely help me to decide if I should take the grad quantum mechanics course this coming semester.

Thank you.

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You should probably feel comfortable with basic material before proceeding to Quantum Mechanics at the graduate level. Math in QM includes a lot of linear algebra, as well as some more advanced material, like the representation theory of Lie Groups. Even if you have a handle on the math, physics isn't always formal, and you will certainly need to have a well-tuned intuition. It sounds like you mostly have the background, just brush up on the basics. –  rotskoff Jun 23 '12 at 17:12
    
Ask your advisor. This is only worth it if you're sure you can write a thesis related to quantum mechanics; otherwise it's a waste of time that should be used for preparing for qualifying exams. –  Potato Jun 23 '12 at 18:23
    
What was your field of study in Math in gra. math. level? Your answer will be different if you studied gemetrical fields or analytic or algebraic, graph theory, ... . –  AmirHosein SadeghiManesh Jan 3 '13 at 4:50
    
Depends on what you mean by "should". If you have to study it for your research, I suppose there is no question asked? Otherwise, if it is an interest, I would say no physics background is ok. For efficiency and clarity, you need to find a book that nails down to the mathematical foundations of QM while connecting to experiments. I just do not know any. Make a post to ask for that perhaps? –  Argyll Sep 16 at 1:36

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