# Confusion about state of a quantum system

I am confused with the concept of state of a quantum system. First postulate of QM ussualy says that the wave function of the system contains all information about the state of the system. But reading Dirac's Principles of QM made me think that state of the system always corresponds to some specific observable we want to measure. For example consider spin-1/2 particle. If We are interested in the spin in z-direction then corresponding state $| \psi \rangle$ of the system is a superposition of all eigenvalues of the operator $S_z$, i.e. $| \psi \rangle = c_1 | \uparrow \rangle + c_2 | \downarrow \rangle$ for some $c_1,c_2 \in \mathbb{C}$. So corresponding state space of such particle is two-dimensional Hilbert space $H =$Span$\{ | \uparrow \rangle , | \downarrow \rangle \}$. And if we were interested in some different observable, we might have different state space. So it appears to me that state of a quantum system always corresponds to some specific observable - is that correct?

• Hi AlanHarper, and welcome to Physics Stack Exchange! We prefer to have one question asked per post, so could you perhaps remove the second question from this post and put it up separately? – David Z Mar 13 '14 at 16:47