Quasi-Landau Spectrum of the Chaotic Diamagnetic Hydrogen Atom

The highly excited hydrogen atom in static magnetic fields has been in recent years a subject of intense experimental [1–4] and theoretical [4–9] studies which have led to substantial progress in the understanding of this previously unsolved elementary problem. Described by the Hamiltonian (in atomic units) $$H=\frac{1}{2}{{P}^{2}}+\frac{1}{2}\gamma {{L}_{z}}+\frac{1}{8}{{\gamma }^{2}}{{\rho }^{2}}-\frac{1}{\gamma }$$ (1) (cylindrical coordinates, r = (ρ2 + z2)½ field parameter γ = B/Bo with Bo = 2.35 × 105 Tesla) the magnetized atom is of particular interest in the quasiLandau regime of strong mixing of the Coulomb and diamagnetic interactions, i.e. where the two forces are of comparable strength. In this regime the motion of the Rydberg electron becomes classically chaotic [10]. It is this aspect which has recently attracted much attention, as the magnetized atom constitutes an ideal model case for detailed experimental studies of the quantum mechanics of a most simple atomic system in classical chaos.