  We formulate a self-consistent model of the integer quantum Hall effect on an
infinite strip, using boundary conditions to investigate the influence of
finite-size effects on the Hall conductivity. By exploiting the translation
symmetry along the strip, we determine both the general spectral properties of
the system for a large class of boundary conditions respecting such symmetry,
and the full spectrum for (fibered) Robin boundary conditions. In particular,
we find that the latter introduce a new kind of states with no classical
analogues, and add a finer structure to the quantization pattern of the Hall
conductivity. Moreover, our model also predicts the breakdown of the quantum
Hall effect at high values of the applied electric field.
