Study quantum mechanics without physics background

Question

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 another 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.

Answer 1

You may find my book Classical and quantum mechanics via Lie algebras useful. It doesn't assume any prior knowledge of physics (except at places where you can skip it without harm) and develops on the fly whatever is needed.

Answer 2

Do I need to prepare more before taking graduate Quantum Mechanics?

As an EE grad student, I once enrolled in the first of a graduate class series on QM. On the first day, the professor asked for a show of hands indicating what undergraduate courses on QM had been taken by the students in the class. He was surprised that I and another student had not taken any undergraduate QM classes so he asked to see us after class.

He was very cordial but frankly asked us to reconsider taking his class. He pulled out some of the early homework sets which were, he said, review. I recognized very little of it despite having casually studied some QM texts in years past.

So, after having given that preface, I'll give you my advice. Take an undergraduate class or three in QM to prepare for graduate QM.

Answer 3

I would avoid the Feynman Lectures for QM. Griffiths is probably your best option. Newer editions have a nice appendix on Linear Algebra. It doesn't assume knowledge of partial differentials. Partial Differential Equations for Scientists and Engineers by Farlow is a great intro to PDEs.

Answer 4

With a computer science background, you may appreciate the following "physics-free" introductions to quantum computing for computer scientists:

• L. Fortnow, One complexity theorist's view of quantum computing
• S. Fenner, A Physics-Free Introduction to the Quantum Computation Model

For a more in-depth introduction, the standard text is

• Nielsen, Chuang, Quantum Computation and Quantum Information

This textbook also requires only a very limited physics background. The basic tool of theoretical quantum computing research is certainly linear algebra. Once you have covered the basics, I would also recommend some matrix analysis book, such as Horn & Johnson's.