2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/17554We introduce s.n where n is the unit vector in the direction of the radius vector and s is the spin, which along with the velocity forms a spin-orbit interaction of the order of v/c whereas the usual spin-orbit interaction is of the order of the square of v/c. The effective fractional charges obtained from this interaction are in good agreement with the experimental data of the quantum Hall effect. The energy of the system diverges as L tends to infinity indicating that there is a phase transformation at the half-filled Landau level.8 pagesMesoscale and Nanoscale Physicstext