The theory of quantum mechanics continues to appear arbitrary and abstruse to new students; and to many veterans, it has become acceptable and useable only because it is familiar. Yet, this theory is at the basis of all modern physics, chem­ istry, and engineering, describing, as it does, the behavior of the submicroscopic particles making up all matter. So it needs to be presented more effectively to a diverse audience. The primary question is, I believe, 'What can be considered self-evident?' Indeed, what do certain key experiments reveal about the workings of nature? How can we consider that some probabilities are not a result of our ignorance, but instead, fundamental properties? We must pay particular attention to the subject of what we can do, what we cannot do, and what we can and cannot observe. We can prepare a homogeneous beam of almost independent particles by boiling electrons out of a metal and accelerating them by a given potential drop. We cannot follow an electron in­ dividually in the beam without introducing conditions that destroy the beam's homogeneity, but we can detennine when electrons arrive at a given position.