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my first post here. I apologize, if i make something stupid.

I am a third year undergraduate. I took a course in quantum mechanics last semester, and i am taking one more course this semester, and i must admit, i am not very fluent in the realm of quantum mechanics.

my question is rather basic. I was rereading the book "Quantum mechanics, concepts and applications" by Nouredine Zettili. WHile many of my colleagues say this is a "basic" book, i like it, because it helps me to build concepts.

When studying the state vectors, i reminded myself about the phase space in classical physics. a link here: http://en.wikipedia.org/wiki/Phase_space

I was wondering, the reason one wants to deal with the phase space is that, it is a complete space which encloses the position and momnetum vectors. But to the best of my knowledge, it does not include any mathematical operation (addition and multiplication can be applied on it, but does the definition of the phase space include these?).

My question is, is the reason why one wants to calculate state vector the same as above, that because it encloses the position and momentums of the system? also, as the name implies, the state vector is not the space of all possible momentum/positions. is there the notation of such a space which encloses all momentum and positions? does that space encloses the mathematical operations? [bzw. operators]

sorry for the entry level question, but often the professor is too busy to answer it.