Amplitude phase-space model for quantum mechanics

It is shown that there is a close relationship between quantum mechanics and ordinary probability theory. The main difference is that in quantum mechanics the probability is computed in terms of an amplitude function, while in probability theory a probability distribution is used. Applying this idea, an amplitude model for quantum mechanics on phase space is constructed. In this model states are represented by amplitude functions and observables are represented by functions on phase space. If a conjugation condition is postulated the model provides the same predictions as conventional quantum mechanics. In particular, the usual quantum marginal probabilities, conditional probabilities and expectations are obtained. The commutation relations and uncertainty principle also follow. Moreover Schroedinger's equation is shown to be an averaged version of Hamilton's equation in classical mechanics. (author)