The domain of the quantum matter wave

In quantum mechanics a particle is represented by a complex wave function. This is similar to the classical description of a distributed particle by a real valued density function. However, while classically the combined density of multiple particles can be decomposed into individual densities; the wave function of a multi-particle system can not always be decomposed into wave functions for the individual particles. Hence the classical assumption that density is a property of physical space, which is only possible because of the special topology of classical configuration space, does not work for quantum systems. (orig.)