R. de la Madrid The Rigged Hilbert Space of the Free Hamiltonian (53K, Latex) ABSTRACT. We explicitly construct the Rigged Hilbert Space (RHS) of the free Hamiltonian $H_0$. The construction of the RHS of $H_0$ provides yet another opportunity to see that when continuous spectrum is present, the solutions of the Schr\"odinger equation lie in a RHS rather than just in a Hilbert space.