IJPAM: Volume 2, No. 3 (2002)
ELECTRONS IN ONE-DIMENSIONAL CONFINEMENTS
Institute of Industrial Science
The University of Tokyo, Meguro-ku
Tokyo 153-8505, JAPAN
Dept. of Applied Physics
Graduate School of Engineering
Osaka University, 2-1 Jamadaoka, Suita
Osaka 565-0871, JAPAN
Abstract.We study the ground state behavior/properties of a system of interacting electrons confined one-dimensionally. To describe the system, we first derive a set of fundamental equations with the aid of the Bethe ansatz method. We then obtain an exact numerical solution for this set of fundamental equations to determine the ground state energy/properties for a few electrons inside a one-dimensional confinement. On the basis of the obtained results, we discuss the effects of the electron-electron interaction on the ground state properties of the system of interacting electrons confined in one-dimension. We also compare the results derived by imposing periodic boundary conditions, to those derived by imposing that the electrons are (one dimensionally) confined by infinitely high potential walls (hard walls). From these results, we can conclude that a proper description of the boundary conditions is indeed necessary for a correct estimation of the effect of the electron-electron interaction.
This should lead us to a correct interpretation of the electron dynamics, and proper evaluation of the functionalities of novel materials based on this system.
Received: April 1, 2002
AMS Subject Classification: 00A79, 70E45, 70E55, 70F10, 74H05, 81Q05
Key Words and Phrases: electron density, many body and quasi-particle theories, quantum effects, quantum wells
Source: International Journal of Pure and Applied Mathematics