TY - JOUR
T1 - 1D periodic potentials with gaps vanishing at k=0
JF - Mem. Differential Equations Math. Phys. 47 (2009) 133-158
Y1 - 2009
A1 - Alessandro Michelangeli
A1 - Osvaldo Zagordi
AB - Appearance 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 SchrÃ¶dinger equation (Hill\\\'s equation). This result is placed in the perspective of the previous related results available in the literature.
UR - http://hdl.handle.net/1963/1818
U1 - 2396
U2 - Mathematics
U3 - Mathematical Physics
ER -