We've been assigned Griffiths QM for undergraduate physics. I don't particularly like it, but anyway. It says that if the eigenvalues an observable are continuous then the eigenfunctions do not represent physically realisable states. So the eigenfunctions of the hamiltonian are discrete and therefore the stationary states represent real states. But for the position operator for example which must have the eigenfunction of the form g(x)=A dirac delta(x-y), this is continuous and hence is not a physically realisable state. But I thought when you make a measurement on a wave function is collapses to exactly that the dirac delta function, which would indicate this does actually occur physically. Or does this just say that this is not a physically realisable wave function given it is not dependent on time and just sits there as at a point for all eternity? Haha thanks.