  This article presents some controllability and stabilization results for a
system of two coupled linear Schr\"odinger equations in the one-dimensional
case where the state components are interacting through the Kirchhoff boundary
conditions. Considering the system in a bounded domain, the null boundary
controllability result is shown. The result is achieved thanks to a new
Carleman estimate, which ensures a boundary observation. Additionally, this
boundary observation together with some trace estimates, helps us to use the
Gramian approach, with a suitable choice of feedback law, to prove that the
system under consideration decays exponentially to zero at least as fast as the
function $e^{-2\omega t}$ for some $\omega>0$.
