Separability is a mathematically convenient hypothesis, with the physical interpretation that the state is uniquely determined by countably many observations. Quantum states can be identified with equivalence classes in H, where two vectors (of length 1) represent the same state if they differ only by a phase factor. As such, quantum states form a ray in projective Hilbert space, not a vector. Many textbooks fail to make this distinction, which could be partly a result of the fact that the Schrödinger equation itself involves Hilbert-space "vectors", with the result that the imprecise use of "state vector" rather than ray is very difficult to avoid.