Ju l 2 00 4 Lamé polynomials , hyperelliptic reductions and Lamé band structure

  title={Ju l 2 00 4 Lam{\'e} polynomials , hyperelliptic reductions and Lam{\'e} band structure},
  author={Robert S. Maier},
The band structure of the Lamé equation, viewed as a one-dimensional Schrödinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l = 1 dispersion relation, and a previously published l = 2 dispersion relation is shown to be partly incorrect. The Hermite–Krichever Ansatz, which expresses Lamé equation solutions in terms of l = 1 solutions, is the chief tool. It is based on a projection from a genus-l… CONTINUE READING