  We consider a general symplectic transformation (also known as linear
canonical transformation) of quantum-mechanical observables in a quantized
version of a finite-dimensional system with configuration space isomorphic to $
\mathbb{R}^{q} $. Using the formalism of rigged Hilbert spaces, we define
eigenstates for all the observables. Then we work out the explicit form of the
corresponding transformation of these eigenstates. A few examples are included
at the end of the paper.
