  This paper deals with the Schr{\"o}dinger equation $i\partial_s u({\bf
z},t;s)-\cal L u({\bf z}, t;s)=0,$ where $\cal L$ is the sub-Laplacian on the
Heisenberg group. Assume that the initial data $f$ satisfies $| f({\bf z},t)|
\leq C q_a({\bf z},t),$ where $q_s$ is the heat kernel associated to $\cal L.$
If in addition $ |u({\bf z},t;s_0)|\leq C q_b({\bf z},t),$ for some $s_0\in
\R^*,$ then we prove that $u({\bf z},t;s)=0$ for all $s\in \R $ whenever
$ab<s_0^2.$ This result also holds true on $H$-type groups.
