Postulate 1

A quantum system state is represented by a unit vector $\psi$ in a Quantum Hilbert Space $H$.

These are unique up to multiples of unity, i.e. ${\psi }_1$ and ${\psi }_2$ represent the same physical state whenever $\exists c\in \mathbb{C},\Vert c\Vert =1$ such that ${\psi }_1=c{\psi }_2$ .