Sorry for a (maybe) dumb question, but... I understand that according to QM, the description of the situation for a particle or system is described by a linear superposition of the wave functions of all the possible states (eigenstates) of the system. When a measurement is made, the wave function, according to garden variety QM, "collapses" to the state measured. The probability of getting a particular result is proportional to the usual square (in the complex sense) of the wave function corresponding to the eigenvector for the state measured. All that being said, it seems to me that there are reasonable scenarios which do not require this composite wave function, nor its collapse. Let me lay out my thoughts for someone to attack... If the system is simply in a single state, then the measurement identifies (measures) that state. If I make multiple measurements over a large sample of equivalent systems, I get a distribution of results. QM would say that is because of the nature of the composite wave function. An equally good, and much simpler explanation is that I am simply drawing results from systems already in different single eigenstates, and the distribution I get simply reflects the distribution of eigenstates in the sample population. For the situation I am describing, there is no way to tell the difference between these explanations. Maybe here, the composite wave function is simply an artifact of the QM formalism???