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Originally proposed by Read [1] and Jain [2], the so-called"composite-fermion" is a phenomenological attachment of two infinitely thinlocal flux quanta seen as nonlocal vortices to two-dimensional (2D) electronsembedded in a strong orthogonal magnetic field. In this letter, it is describedas a highly-nonlinear and coherent mean-field quantum process of the solitontype by use of a 2D stationary Schroedinger-Poisson differential model withonly two Coulomb-interacting electrons. At filling factor $\nu={1}{3}$ of thelowest Landau level, it agrees with both the exact two-electron antisymmetricSchroedinger wave function and Laughlin's Jastrow-type guess for the fractionalquantum Hall effect, hence providing this later with a tentative physicaljustification based on first principles.

Coherent Nonlinear Quantum Model for Composite Fermions