Prof. Manuel Gadelha
Symposium on Mathematical Problems in Quantum Mechanics
UEPG, 4th of September 2023
Centro Integrar, Room 9
Quantum Mechanics, one of the pillars of modern physics, is a rich source of mathematical problems. For example, the widely used Dirac formalism, based on bras and kets, lacks mathematical rigor; the usual treatment of singular interactions leads, in general, to mathematically ill-defined products that need posterior regularization and sometimes renormalization of infinite quantities, etc. To address these, and other, mathematical problems present in the quantum theory several mathematically rigorous approaches have been proposed in the literature, such as rigged Hilbert spaces (RHS), self-adjoint extensions of symmetric operators, and theory of distributions, among others.
This symposium, organized on the occasion of the scientific visit of Prof. Manuel Gadella at UEPG, intends to bring together local researchers in the field of mathematical physics and its interfaces to discuss some of the above-mentioned approaches, as well as other closely related problems in quantum mechanics.
Prof. Gadella, from Departamento de Física Teórica, Atómica y Óptica and Instituto de Investigación en Matemáticas – Universidad de Valladolid, Spain, is a renowned researcher in the field of mathematical physics who has made many significant contributions to the field along his career. For instance, he worked on problems concerning mathematically rigorous formulations for the Dirac formalism in quantum mechanics based on rigged Hilbert spaces. He also made important contributions to the study of Gamow states, contact interactions, Casimir effect, special functions, Lie groups and algebras, self-adjoint extensions of symmetric operators, and so on.
