Group Theory Approach to Band Structure: Scarf and Lame Hamiltonians
Condensed Matter
2009-10-31 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
solv-int
Abstract
The group theoretical treatment of bound and scattering state problems is extended to include band structure. We show that one can realize Hamiltonians with periodic potentials as dynamical symmetries, where representation theory provides analytic solutions, or which can be treated with more general spectrum generating algebraic methods. We find dynamical symmetries for which we derive the transfer matrices and dispersion relations. Both compact and non-compact groups are found to play a role.
Keywords
Cite
@article{arxiv.cond-mat/9907202,
title = {Group Theory Approach to Band Structure: Scarf and Lame Hamiltonians},
author = {Hui Li and Dimitri Kusnezov},
journal= {arXiv preprint arXiv:cond-mat/9907202},
year = {2009}
}
Comments
4 pages + 2 figs. Revtex/epsf. To appear: Phys Rev Lett, v.83 1999