An exactly solvable non C¹ periodic potential

In this paper, we are concerned with the study of the spectrum of a periodic potential in 1D, modelling the interactions of an electron with a regular lattice of ions. The classical Bloch theory asserts that the spectrum has a band structure. In the case of a sawtooth potential, we have a very precise description and estimates of all bands and of all gaps under the potential barrier and near the minimum of the potential. (authors)