Centre-of-mass motion in multi-particle Schroedinger-Newton dynamics

We investigate the implication of the non-linear and non-local multi-particle Schroedinger-Newton equation for the motion of the mass centre of an extended multi-particle object, giving self-contained and comprehensible derivations. In particular, we discuss two opposite limiting cases. In the first case, the width of the centre-of-mass wave packet is assumed much larger than the actual extent of the object, in the second case it is assumed much smaller. Both cases result in non-linear deviations from ordinary free Schroedinger evolution for the centre of mass. On a general conceptual level we include some discussion in order to clarify the physical basis and intention for studying the Schroedinger-Newton equation.