An Axiomatic Approach to the Formalism of Quantum Mechanics. I.

Abstract

An axiomatic formulation of a quantum mechanical formalism is given. The formulation is not in terms of objects associated with the Hilbert space, but in terms of a different kind of objects for which the name ``complex probability measures'' has been chosen. It is shown that the conventional Hilbert‐space formalism obeys the given axioms. A few consequences of the axioms are investigated, some of which are found useful in the second part of this work.