Dynamical Symmetry Approach to Periodic Hamiltonians

Details Dynamical Symmetry Approach to Periodic Hamiltonians Dynamical Symmetry Approach to Periodic Hamiltonians

1999-12-06

arxiv.org/abs/solv-int/9912007v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

20 pages, 7 postscript figures

Scientific paper

10.1063/1.533265

We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy bands and gaps are readily understood in terms of representation theory. We compute the transfer matrices and dispersion relations for these systems, and find that the complementary series plays a central role as well as non-unitary representations.

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