In his splendid paper “The nature of elementary particle” Schroedinger proposes a few very keen ontological intuitions about the object of quantum mechanics. First he formulates a very clear common-sense example in order to explain quantum statistics. Let us imagine that a teacher wants rewarding Tom, Jerry and Sara. In the first situation he has one old coin with the portrait of Newton and another with the portrait of Shakespeare. Therefore the teacher could give both coins to Tom, both to Jerry and both to Sara. Moreover he has other six ways of distributing one coin to two children. In the metaphor the two coins are particles and the three pupils are possible states of the particles. This is classical Boltzmann-Maxwell statistics. In the second situation the teacher has two one-euro coins. Therefore, as before, he can give both coins to Tom, both to Jerry and both to Sara. But now he has only three ways of distributing the two coins to two of the three children, since the two coins are indistinguishable. This is Bose-Einstein statistics. In the third situation the teacher could give as reward two holidays in the same place and at the same conditions next week. Now he cannot give both prizes to the same pupil and the two holidays are indistinguishable as in the second case. Therefore the teacher has only three possibilities of distributing one holiday to two of the three children. This is Fermi-Dirac statistics.
A second point emphasized by Schroedinger is very interesting. Looking at a particle which crosses a Wilson Chamber, someone could say “Here it is the precise trajectory of a particle, against wave-particle dualism!”. Indeed what we are seeing is not THE particle, but a series of very similar states that a NOT COMPLETELY INDIVIDUATED particle could assume at different times.