1D periodic potentials with gaps vanishing at k=0

Details 1D periodic potentials with gaps vanishing at k=0 1D periodic potentials with gaps vanishing at k=0

2006-03-07

arxiv.org/abs/cond-mat/0603172v4

Mem. Differential Equations Math. Phys. 47 (2009), pp. 133-158

Physics

Condensed Matter

Other Condensed Matter

29 pages, 4 figures, version accepted for publication in Memoirs on Differential Equations and Mathematical Physics

Scientific paper

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 characterize them through 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 occur of linearly independent solutions of the corresponding Schroedinger equation (Hill's equation). This result is placed in perspective of the previous related results available in the literature.

Affiliated with

Also associated with

No associations

Rating

1D periodic potentials with gaps vanishing at k=0 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with 1D periodic potentials with gaps vanishing at k=0, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and 1D periodic potentials with gaps vanishing at k=0 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-365926