Abstract
The negative hydrogenic ion is not only of physical but also historic importance for it is the first quantum mechanical three-body problem that involves the intrinsic electron-electron correlation. Recent advances in nanotechnology have brought the study of this system in a quantum wire into the forefront. The nonanalytic behaviors of the binding energy of the second electron in a negative hydrogenic ion in one dimension and in a quantum wire (QWR) as a function of the Coulombic repulsive strength and the wire radius are first identified. They are then exploited, together with the recognition of the well-known near-infinite (à la Loudon) binding energy of the neutral hydrogenic atom, to set up a model that calculates in a QWR directly, thereby avoiding the pitfalls of a variational approach to this problem. This , found to be , is an exact solution for a wire whose radius is nearly zero. For a finite , it is shown that still , which is independent of as long as due to the inverse square nature of the Coulomb force. Its comparisons with the corresponding cases in three dimensions and two dimensions is discussed.
- Received 24 June 2005
DOI:https://doi.org/10.1103/PhysRevB.72.153303
©2005 American Physical Society