As to the bulk of your question, which I take to be a reference request for mathematical accounts of quantum mechanics, I am partial to the book [Quantum Mechanics for Mathematicians](http://www.amazon.com/Quantum-Mechanics-Mathematicians-Graduate-Mathematics/dp/0821846302) by L. Takhtajan.

Be sure to look over the MathOverflow thread [Where does a math person go to learn quantum mechanics?](https://mathoverflow.net/questions/2917/where-does-a-math-person-go-to-learn-quantum-mechanics), as it contains many good references.