Does anyone have any good suggestions for a QM book at the advanced undergrad level? I am interested in particular about the QM formulation using density matrices as states and POVM's as measurements. I am an engineering student, so my math background isn't too strong beyond the basic linear algebra/calculus 1-2-3 courses. No analysis or abstract algebra or anything like that, so I would actually like a QM book that can also explain the math, kind of like Shankar... except Shankar doesn't even cover PVM's as I recall (I might be wrong though). Thanks in advance for any suggestions!
I don't know of any standard quantum mechanics book that explains POVM's and PVM's. I do have a functional analysis book that treats projection-valued measures, but this book assumes prerequisites like real analysis, measure theory, Hilbert spaces, etc. Where did you hear about them? Lectures on Quantum Theory: Mathematical and Structural Foundations is a nice little book that might interest you. Check out the links for the detailed table of contents and the scope of the book (Chapter 1.1). Density matrices are treated in 6.1 and 6.4.4.
Thanks for the suggestion George, I will check that book out. As for how did I hear about these things, PVM's were covered in my third year QM course. Now, I am doing research in a quantum cryptography group, and although I will mostly be working in the lab, I'd like to have a better understanding of the theory behind what I'm doing... and most of the papers I've seen use density matrices and POVM's.