I'm otherwise pretty comfortable with the postulates of quantum mechanics, but I find it difficult to understand situations where a measurement causes only incomplete collapse of the wave function... Suppose we have an electron in a state described by some wave function. Then we measure its position. If the QM postulates were taken literally, the measurement should collapse the wavefunction into a position eigenstate, a Dirac delta function, that is. But that would be against energy conservation, because an electron in a position eigenstate can have *any* value of kinetic energy with equal probability. I think the position measurement collapses the wavefunction into some kind of an almost-position-eigenstate, like a gaussian spike that is narrow if the position was measured very accurately and wide if the measurement was inaccurate. To measure the position accurately, we should scatter something with very short De Broglie wavelength and very high energy off the electron, which explains the uncertainty in the electrons momentum after the measurement. Probably an inaccurate measurement of the total energy of a molecule could also collapse the molecular wavefunction into a state that is still a superposition of several eigenstates of the Hamiltonian. I don't really understand this, because the postulates don't tell how to handle these kinds of situations. I think this has something to do with the concept of a 'weak' or 'nondemolition' measurement.