Lie point symmetries and the geodesic approximation for the Schrödinger-Newton equations

Oliver Robertshaw, Paul Tod

Published 2005-09-28Version 1

We consider two problems arising in the study of the Schr\"odinger-Newton equations. The first is to find their Lie point symmetries. The second, as an application of the first, is to investigate an approximate solution corresponding to widely separated lumps of probability. The lumps are found to move like point particles under a mutual inverse-square law of attraction.