Perturbations of Periodic Sturm-Liouville Operators

Explore a 37-minute lecture on perturbations of periodic Sturm-Liouville operators delivered by Carsten Trunk from TU Ilmenau, Germany. Delve into the historical context of Hill's equation and its applications in describing atomic nuclei behavior in crystals. Examine the spectral parameter λ and its physical interpretation as electron energy, along with the band structure of essential spectrum. Investigate how impurities (perturbations) can create additional discrete energy levels in forbidden regions. Learn about the changes in spectrum under L1-assumptions on coefficient differences, including descriptions of essential and absolutely continuous spectra of perturbed operators. Discover how finite first moment conditions for coefficient differences limit the number of eigenvalues in spectral gaps, extending Rofe-Beketov's seminal work from the 1960s. Gain insights from this collaborative research involving J. Behrndt, P. Schmitz, and G. Teschl.