A Tentative Completion of Quantum Mechanics

We review a proposal of how to complete non-relativistic Quantum Mechanics to a physically meaningful, mathematically precise and logically coherent theory. This proposal has been dubbed \textit{ETH - Approach} to Quantum Mechanics, ``$E$'' standing for ``Events,'' ``$T$'' for ``Trees,'' and ``$H$'' for ``Histories.'' The $ETH$ - Approach supplies the last one of three pillars Quantum Mechanics can be constructed upon in such a way that its foundations are solid and stable. Two of these pillars are well known. The third one has been proposed quite recently; it implies a general non-linear stochastic \textit{law} for the time-evolution of states of \textit{individual} physical systems. We illustrate the general ideas and results by sketching an application to the quantum theory of \textit{fluorescence} of an atom coupled to the radiation field (in a limit where the velocity of light tends to $\infty$).