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An effective Chern-Simons theory for the quantum Hall states with edges isstudied by treating the edge and bulk properties in a unified fashion. An exactsteady-state solution is obtained for a half-plane geometry using theWiener-Hopf method. For a Hall bar with finite width, it is proved that thecharge and current distributions do not have a diverging singularity. It isshown that there exists only a single mode even for the hierarchical states,and the mode is not localized exponentially near the edges. Thus this resultdiffers from the edge picture in which electrons are treated as strictly onedimensional chiral Luttinger liquids.Comment: 21 pages, REV TeX fil

Current and charge distributions of the fractional quantum Hall liquids with edges