Beyond the Wigner Distribution: Schr{\"o}dinger Equations and Terrace Width Distributions

The so-called generalized Wigner distribution has earlier been shown to be an excellent approximation for the terrace width distribution (TWD) of vicinal surfaces characterized by step-step interactions that are perpendicular to the average step direction and fall off as the inverse square of the step spacing. In this paper we show that the generalized Wigner distribution corresponds to a mean-field treatment of a single step, discuss generalizations to more general step-step interactions, and show that the mean-field predictions are in good agreement with TWDs derived from numerical transfer-matrix calculations and Monte Carlo simulations. We also show that this mean-field treatment allows the step-step interaction to be extracted from experimental TWDs.