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Explore a lecture on quantum Hamiltonians for systems with zero range interactions, focusing on three-body systems. Delve into the challenges of mathematically constructing these Hamiltonians for three or more particles in three dimensions. Examine the Ter-Martirosyan Skornyakov (TMS) Hamiltonian and the associated Thomas effect. Learn about a regularized version of the TMS Hamiltonian that addresses these issues, based on work by Minlos, Faddeev, Albeverio, Høegh-Krohn, and Wu. Discover how this self-adjoint, bounded Hamiltonian emerges as the norm resolvent limit of Hamiltonians with rescaled non-local interactions. Gain insights from this collaborative research involving Giulia Basti, Domenico Finco, and Alessandro Teta, presented at the Workshop on "Spectral Theory of Differential Operators in Quantum Theory" at the Erwin Schrödinger International Institute for Mathematics and Physics.
