Feynman's transition amplitudes in the space Sn?

In this paper we propose a rigorous formulation for Feynman’s propagator\nof Quantum Mechanics; the space in which we build up the propagator is the space of\ntempered distributions S0n .\nThe goals of the paper are the following ones:\n1) a rigorous and operative definition of Feynman’s propagator in S0n;\n2) the basic indications for a straightforward and not-ambiguous calculus for the propagators, easy to teach and use;\n3) a rigorous formulation and proof of the famous Feynman’s Transition Amplitudes Theorem, in the space of tempered distributions; and of one its original generalization.