Blurred orbits and blurred particles: Heisenberg's 1926 helium atom

This work analyses the extent to which the "blurred orbits" of the current model for the atom, drafted by Heisenberg in 1926, fits the image of a bunch of wandering electrons around a nucleus. We will deal with early appearances of the concept of indistinguishable particles within the frame of quantum mechanics. There are few studies on the use of this concept in Heisenberg's 1926 papers on helium, in contrast with the large number of them on its use in Bose--Einstein's 1924 papers. We will discuss to what extent Heisenberg's approach leads to a purely statistical interpretation of this concept. We will also study the viewpoint of Dirac, who dealt with the same topic few months later. Although the indistinguishability of the electrons and indeterminacy are common explanations for the blurring of electron orbits, we argue that such an image is an oversimplification which masks interesting aspects of: a) the dynamics of bound electrons and b) the deeper implications of indistinguishability in quantum mechanics.