Hydrogen atom as a quantum-classical hybrid system

6th International Workshop DICE2012 Spacetime – Matter – Quantum Mechanics: From the Planck Scale to Emergent Phenomena

物理学;力学

Zhan, Fei^1,2 ; Wu, Biao^1

International Center for Quantum Materials, Peking University, 100871, Beijing, China^1

Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, St Lucia, QLD 4072, Australia^2

关键词: Classical object;    Conservation of momentum;    Electron dynamics;    Hybrid description;    Mean field approach;    Quantum counterpart;    Quantum description;    Quantum-classical;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/442/1/012006/pdf
DOI  :  10.1088/1742-6596/442/1/012006

学科分类：力学，机械学

来源: IOP

【 摘 要 】

Hydrogen atom is studied as a quantum-classical hybrid system, where the proton is treated as a classical object while the electron is regarded as a quantum object. We use a well known mean-field approach to describe this hybrid hydrogen atom; the resulting dynamics for the electron and the proton is compared to their full quantum dynamics. The electron dynamics in the hybrid description is found to be only marginally different from its full quantum counterpart. The situation is very different for the proton: in the hybrid description, the proton behaves like a free particle; in the fully quantum description, the wave packet center of the proton orbits around the center of mass. Furthermore, we find that the failure to describe the proton dynamics properly can be regarded as a manifestation of the fact that there is no conservation of momentum in the mean-field hybrid approach. We expect that such a failure is a common feature for all existing approaches for quantum-classical hybrid systems of Born-Oppenheimer type.