  In this note I discuss some aspects of a formulation of quantum mechanics
based entirely on the Jordan algebra of observables. After reviewing some facts
of the formulation in the \CS -approach I present a Jordan-algebraic Hilbert
space construction (inspired by the usual GNS-construction), thereby obtaining
a real Hilbert space and a (Jordan-) representation of the algebra of
observables on this space. Taking the usual case as a guideline I subsequently
derive a Schr\"odinger equation on this Hilbert space.
