Seminarium KMMF "Teoria Dwoistości"

1-dimensional Schr\"odinger operators whose potentials are singular at one of endpoints are very common in applications. I will discuss how to describe their boundary conditions. I will give various examples such as Bessel Hamiltonians, radial Coulomb Hamiltonian, perturbed Bessel Hamiltonians. It is often natural to organize them in holomorphic families, which have sometimes surprising properties.