01174nas a2200109   4500008004300000245005400043210005300097520082800150100002900978700002101007856003601028       2009                        en_Ud  00a1D periodic potentials with gaps vanishing at k=00 a1D periodic potentials with gaps vanishing at k03 aAppearance of energy bands and gaps in the dispersion relations of a periodic potential is a standard feature of Quantum Mechanics. We investigate the class of one-dimensional periodic potentials for which all gaps vanish at the center of the Brillouin zone. We characterise themthrough a necessary and sufficient condition. Potentials of the form we focus on arise in different fields of Physics, from supersymmetric Quantum Mechanics, to Korteweg-de Vries equation theory and classical diffusion problems. The O.D.E. counterpart to this problem is the characterisation of periodic potentials for which coexistence occurs of linearly independent solutions of the corresponding Schrödinger equation (Hill\\\'s equation). This result is placed in the perspective of the previous related results available in the literature.1 aMichelangeli, Alessandro1 aZagordi, Osvaldo  uhttp://hdl.handle.net/1963/1818