Hydrogen Atom Near an Impenetrable Hyperboloidal Surface

C. Yang ； W. Y. Chen ； C. T. Kuo

《Chinese Journal of Physics》 32卷2期 (1994/04) Pp. 97-118

並列摘要

The quantum states of a hydrogen atom located at the focus of an impenetrable hyperboloidal surface of revolution are investigated. It is found that with the decrease of the distance from the nucleus to the surface and/or with the decrease (increase) of the eccentricity of the concave (convex) hyperboloidal surface the eigenenergies of ground and excited states increase monotonously. Several observable physical quantities, namely, the electric dipole moment, the nuclear magnetic shielding, the polarizability and the electron probability density are calculated as functions of the atom's position and the shape of the surface. The obtained results can be entirely understood if one recognizes that the atomic electron is ”pushed away” by an impenetrable surface and in a state with higher energy its probability density spreads wider. So the nearer the surface is and/or the higher the state energy is, the larger is the surface influence. But the influence of the convex surfaces has many features different from that of the concave and plane surfaces. In particular, the electric dipole moment may change its direction and the polarizability may have a significant maximum for excited states at some distances to the surface.