I recently read that a quantum state is actually defined by a ray and not a vector. That is it is possible to multiply a state $\psi$ by any complex number c and you won't be changing the physics in any way. I understand this mThematically, but I don't understand what the physical meaning of such an "equivalent state" would be since the new state need not be normalised if c is not of the form $e^{i\phi}$.  Thanks!