My field of study is computer science, and I recently had some readings on quantum physics and computation.
This is surely a basic question for the physics researcher, but the answer helps me a lot to get a better understanding of the formulas, rather than regarding them "as is."
Whenever I read an introductory text on quantum mechanics, it says that the states are demonstrated by vectors, and the operators are Hermitian matrices. It then describes the algebra of vector and matrix spaces, and proceeds.
I don't have any problem with the mathematics of quantum mechanics, but I don't understand the philosophy behind this math. To be more clear, I have the following questions (and the like) in my mind (all related to quantum mechanics):
- Why vector/Hilbert spaces?
- Why Hermitian matrices?
- Why tensor products?
- Why complex numbers?
(and a different question):
- When we talk of an n-dimensional space, what is "n" in the nature? For instance, when measuring the spin of an electron, n is 2. Why 2 and not 3? What does it mean?
Is the answer just "because the nature behaves this way," or there's a more profound explanation?