Group Theory Approach to Band Structure: Scarf and Lame Hamiltonians

Details Group Theory Approach to Band Structure: Scarf and Lame Hamiltonians Group Theory Approach to Band Structure: Scarf and Lame Hamiltonians

1999-07-14

arxiv.org/abs/cond-mat/9907202v1

Physics

Condensed Matter

4 pages + 2 figs. Revtex/epsf. To appear: Phys Rev Lett, v.83 1999

Scientific paper

10.1103/PhysRevLett.83.1283

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.

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