I am a first year PhD math student, and must decide: should I study Quantum Mechanics, although I don't have undergrad background in Physics?
Let me be more specific about my situation:
I'm a first year PhD math student with undergraduate background in Computer science. I switched from Computer Science to Math because I want to study Quantum Computing, in particular involving Quantum Mechanics.
I only learned "general physics" (for non-physicists) in my undergraduate studies, and in particular didn't learn anything about Lagrangians or Hamiltonians, and very little about Maxwell's or Schrödinger's equations; and that was some time ago now besides.
I also don't know anything about Partial Differential Equations, and am planning to review my Linear Algebra.
My math department allows me to take one qualifying exam in Math and the other in another department (though the procedure is rather complicated.) I wish that I could take Quantum Physics as the second qualifying exam, but I should be extremely cautious about this decision. (To me, qual exams in my math department are really challenging, not to mention in other department). Now, I have to take some undergrad courses in math since I did not have math knowledge in undergrad, so if i take physics courses then the time to meet my math degree requirement has to last longer.
I want to study Quantum Information/Computing and in the long term to study Quantum Mechanics. I think the sooner I take the course Quantum Mechanics, the better I study Quantum Information/Computing, but I know everything is not as easy as I expect.
Do I need to prepare more before taking graduate Quantum Mechanics?
Your suggestion, experience will definitely help me to decide. Thank you.