Quantization and Non holomorphic Modular Forms This is a new approach to the theory of non holomorphic modular forms based on ideas from quantization theory or pseudodifferential analysis. Extending the Rankin Selberg method so as to apply it to the calculation of the Roelcke Selberg decomposition of the product of two Eisenstein series one lets Maass cusp forms appear as residues of simple Eisenstein like series. Other results based on quantization theory include a reinterpretation of the Lax Phillips scattering theory for the automorphic wave equation in terms of distributions on R2 automorphic with respect to the linear action of SL(2 Z)