Quantum dynamics of hydrogen atom in complex space

摘要: Abstract We show in this paper that the electron’s quantum dynamics hydrogen atom can be modeled exactly by Hamilton–Jacobi formalism. It is found quantizations of energy, angular momentum, and action variable ∫p dq are all originated from complex motion, shell structure observed indeed potential, which forces acting upon electron uniquely determined, stability atomic configuration justified, trajectories derived accordingly. Based on trajectory, we explain why appears at some positions with large probability, while other small probability. The maximum probability predicted standard mechanics to just stable equilibrium points non-linear dynamics. discovered very diverse strongly state-dependent; them open non-periodic, closed periodic. Over such a great diversity orbits, commensurability condition ensuring existence orbit will de Broglie’s standing wave pattern identified. Along investigation orbits atom, also clarify old using concept classical correctly predict energy quantization meanwhile it not applicable general system. Finally, internal mechanism how precessing, non-conical eigen-trajectories evolve continuously classical, non-precessing, conical as n → ∞ explained detail.