String Theory Journal Club

This talk is based on joint work with Jan Dereziński available on arXiv:2509.03235. In this study, we investigate $6+3$ classes of one-dimensional Schrödinger operators that are solvable in terms of the Gauss hypergeometric function, treated as closed operators. In the first part of the talk, I will motivate this work by reviewing the Laplacian on symmetric Riemannian spaces. Following that, I will briefly revisit key concepts from spectral theory and the theory of hypergeometric functions. Finally, I will present several theorems concerning the Green functions of these operators and discuss the transmutation (a “magical” transformation) identities that connect different families. The aim of the talk is to share some useful ideas and perspectives in a clear manner, with an emphasis on conveying the essential concepts rather than technical details.