Lagrange Equilibrium Points in Celestial Mechanics and Nonspreading Wave Packets for Strongly Driven Rydberg Electrons

We exhibit analytically and confirm numerically the existence of stable, though nonstationary, quantum states of electrons moving on circular orbits that are rapped in an effective potential well made of the Coulomb potential and the rotating electric field produced by a strong circularly polarized electromagnetic wave. These states are direct counterparts of the Trojans—two clusters of asteroids moving around the Sun in the vicinity of the stable Lagrange points in the Sun-Jupiter two-body system.