The (non-relativistic) Schrödinger equation in principle describes the structure of atoms, at least as long as relativistic effects are negligible. It is well-known that in reality the many-body Schrödinger equation is too complex to be solved accurately. We may nevertheless ask more qualitative questions. One such question is to explain the structure of the periodic table of the elements. Fermi attempted, already in 1927, to explain the Aufbau principle ( the order in which atomic orbitals are filled) but did not quite succeed. It turns out, however, that the fundamental nature of the Aufbau principle is, indeed, questionable. I will discuss how Fermi’s result is in some sense accurate even if it disagrees with the Aufbau principle. I will also address the question of the periodicity of the periodic table, i.e., the property that elements in the same group have similar chemical properties. While this is too difficult to understand in the full many-body Schrödinger equation I will analyze it in a simpler mean-field Schrödinger equation.
This is based on joint work with August Bjerg, Soren Fournais, and Peter Hearnshaw.