2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158578The incompressible Quantum Hall strip is sensitive to charging of localized states in the cyclotron gap. We study the effect of localized states by a density functional approach and find electron density and the strip width as a function of the density of states in the gap. Another important effect is electron exchange. By using a model density functional which accounts for negative compressibility of the QH state, we find electron density around the strip. At large exchange, the density profile becomes nonmonotonic, indicating formation of a 1D Wigner crystal at the strip edge. Both effects, localized states and exchange, lead to a substantial increase of the strip width.6 LaTeX pages, 2 postscript figures, to be published in EP2DS proceedingsMesoscale and Nanoscale Physicstext