  The Kepler's third law is a relation between the period and the energy of two
classical particles interacting via a gravitational potential. Recent works
showed that this law could be extended, at least approximately, to classical
three-body systems, or even many-body classical systems. So, a classical quasi
Kepler's third law seems to exist. In this paper, approximate analytical
solutions are computed for quantum self-gravitating particles with different
masses. The results give strong indications in favor of the existence of a
quasi Kepler's third law for such systems. The relevance of the proposal is
checked with accurate numerical data for the ground state of self-gravitating
identical bosons and with numerical estimations for systems with identical
particles plus a different one. Connections between the quantum and classical
systems are discussed.
