  A nonlinear single-particle model is introduced, which captures the
characteristic of systems in the quantum Hall regime. The model entails the
magnetic Shr\"odinger equation with spatially variable magnetic flux density.
The distribution of flux is prescribed via the postulates of the mesoscopic
mechanics (MeM) introduced in my previous articles [cf. J. Phys. Chem. Solids,
65 (2004), 1507-1515; J. Geom. Phys., Vol. 55/1 (2005), 1-18]. The model is
found to imply exact integer and fractional quantization of the Hall
conductance. In fact, Hall resistance is found to be $R_H =
\frac{h}{2e^2}\frac{M}{N}$ at the filling factor value $N/M$. The assumed
geometry of the Hall plate is rectangular. Special properties of the magnetic
Shr\"odinger equation with the mesoscopic feedback loop allow us to demonstrate
quantization of Hall resistance as a direct consequence of charge and flux
quantization. I believe results presented here shed light at the overall status
of the MeM in quantum physics, confirming its validity.
