2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/16488There exists a widely believed opinion, that the many-body ground state of a two-dimensional electron system at a completely filled lowest Landau level (the filling factor $ν=1$) is described by the so-called Hartree-Fock wave function, and that this solution is the unique, exact eigenstate of the system at $ν=1$. I show that this opinion is erroneous, construct an infinite number of other variational many-body wave functions, and discuss the properties of a few states which have the energy substantially lower than the energy of the Hartree-Fock state.REVTeX, 4 pages, 1 figure, some minor changes in the textMesoscale and Nanoscale PhysicsStrongly Correlated Electronstext