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We prove dispersive and Strichartz inequalities for the solution of the wave equation related to the full Laplacian on the Heisenberg group, by means of Besov spaces defined by a Littlewood-Paley decomposition related to the spectral resolution of the full Laplacian. This requires a careful analysis due also to the non-homogeneous nature of the full Laplacian. This result has to be compared to a previous one by Bahouri, Gerard and Xu concerning the solution of the wave equation related to the Kohn-Laplacian.

Strichartz inequalities for the Schrödinger equation with the full Laplacian on the Heisenberg group