Essentials of the Natural Model of the Hydrogen Atom

The usual quantum model for the hydrogen atom is a Hamiltonian dynamical system defined over a complex projective space; it is based on Schrödinger operator H. Since the 1920s it is known that, when compared with the physical atom, the quantum model has important shortcomings. First and foremost the quantum system has no trajectories joining stationary electron configurations at different energy levels, as reflected in Schrödinger phrase "diese verdammte quantenspringerei". The natural model is an alternative Hamiltonian system also based on H but having space of states equal to the cotangent manifold of a real projective space. This is a system with trajectories that join any pair of given stationary electron configurations. The present paper discuses some basic aspects of the natural model