Studying quantum mechanics without physics background
Solution 1:
This answer is quite late, so I'll make it general for those wondering about how to jump into QM with an undergraduate or higher background in math. A word of caution to mathematicians entering the physics realm: though there is a great overlap in material, the emphasis, pedagogy, and approach of a physicist can be quite different than that of a mathematician. You may (or may not) be frustrated by the lack of rigor, and amount of "guesswork and validation" to find the solutions you are required.
The tools widely used in QM include:
- differential equations / partial differential equations
- linear algebra
- vector operations / vector spaces
- basic complex analysis
A great conceptual introduction to the physics of QM can be found here:
- Wikipedia pages (Schrodinger Equation, Quantum Mechancs, and associated wiki links)
- Introduction to Quantum Mechanics (David J. Griffiths).
The latter, in particular, I found quite exceptional. Though other texts may be more complete references, Griffiths makes the physical ideas behind QM very plain and intuitive - something often obscured elsewhere.
As for whether to take the undergraduate or graduate course: My experience is that the undergraduate course will focus more on the conceptual aspects of QM, while the graduate course will assume some of that and focus on more difficult problems; due to this, I personally would recommend beginning with the undergraduate course.
Solution 2:
Chemists and material scientists routinely get an exposure to QM without needing all the courses that a physicist takes. Math through multivar-calc/DiffyQs and first year physics is enough.
Take a look at the QM in a standard p-chem book (say Atkins). http://www.amazon.com/Atkins-Physical-Chemistry-Peter-W/dp/0198792859 pages 249-365
You don't need to learn QM as well as the physicist does or with all the unconscious assumptions of prerequisites. Half a loaf is better than none. You can work your way up to full loaf if worthwhile, later.