Bound states and zero‐energy resonances of one‐dimensional finite periodic potentials are investigated, by means of Levinson’s theorem. For finite range potentials supporting no bound states, a lower bound for the (reduced) time delay at threshold is derived.

Sassoli de Bianchi, M. and Di Ventra, M. (1995). On the number of states bound by one-dimensional finite periodic potentials. J. Math. Phys. 36, pp. 1753-1764. Doi: 10.1063/1.531083.