education - study quantum mechanics without physics background

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:

1. 
   

   Background:
   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.

   
   


2. 
   

   Situation:
   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.

   
   
   


3. 
   

   Expectation:
   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.