Schrödinger Operators with Delta-Potentials on Unbounded Lipschitz Surfaces

Explore Schrödinger operators with delta-potentials on unbounded Lipschitz surfaces in this 27-minute conference talk by Peter Schlosser. Delve into the self-adjoint Schrödinger operator Aα in L2(R^d) with a δ-potential supported on a Lipschitz hypersurface Σ. Learn about the uniqueness of the ground state and the determination of the essential spectrum under specific conditions. Examine the special case of a hyperplane Σ, where a Birman-Schwinger principle with a relativistic Schrödinger operator is obtained. Discover an optimization result for the bottom of the spectrum of Aα as an application. The talk covers the formal operator, its properties, essential spectrum, and proofs, providing a comprehensive overview of this advanced mathematical topic in spectral theory.