On the Spectra of Real and Complex Lamé Operators

William A. Haese-Hill, Martin A. Hallnäs, Alexander P. Veselov

We study Lamé operators of the form $$L=-\frac{d^2}{d{x}^2}+m(m+1){\omega }^2\wp (\omega x+z_0),$$ with $m\in \mathbb{N}$ and $\omega$ a half-period of $\wp (z)$. For rectangular period lattices, we c…