Electron Energy Gaps in a One-Dimensional Liquid

Abstract

The method of Faulkner and Korringa is applied to a one-dimensional liquid in which the atomic potentials are $\delta$ functions and the distances between neighboring atoms satisfy a Gaussian distribution. It is shown that an energy gap exists if $\sigma$, the standard deviation in the Gaussian distribution, is small enough. The behavior of the energy gaps as $\sigma$ is varied agrees very well with the numerical results of Makinson and Roberts.