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.