Time: January 14, 2025, 2:00 pm Place: Room 403, IMI - BAS Speaker: Jean-Pierre Gazeau, Université Paris-Cité Title: Regularized Quantum Motion in a Bounded Set: Hilbertian Aspects Further information: https://icms.bg/regularized-quantum-motion-in-a-bounded-set-hilbertian-aspects-talk-by-jean-pierre-gazeau/ Abstract. It is well known that the momentum operator canonically conjugated to the position operator for a particle confined within a bounded interval of the line (with Dirichlet boundary conditions) is not essentially self-adjoint, as it possesses a continuum of self-adjoint extensions. In this talk, we demonstrate that essential self-adjointness can be restored by symmetrically weighting the momentum operator with a positive bounded function that approximates the indicator function of the given interval. This weighted momentum operator arises naturally from a similarly weighted classical momentum through the Weyl-Heisenberg covariant integral quantization of functions or distributions. Reference: [...]