  In this paper we analyze the evolution of the time averaged energy densities
associated with a family of solutions to a Schr{\"o}dinger equation on a Lie
group of Heisenberg type. We use a semi-classical approach adapted to the
stratified structure of the group and describe the semi-classical measures
(also called quantum limits) that are associated with this family. This allows
us to prove an Egorov's type Theorem describing the quantum evolution of a
pseudodifferential semi-classical operator through the semi-group generated by
a sub-Laplacian.
