Do, 14.11.2019 14:00

Talk by Kyrylo Simonov

Nonstandard analysis meets quantum mechanics

Non-Archimedean mathematics, in particular, nonstandard analysis is an approach based on fields that contain infinitesimal and infinite elements. Within this approach, we construct a space of a particular class of generalized functions, ultrafunctions. The space of ultrafunctions can be used as a richer framework for a description of a physical system in quantum mechanics. In this talk, I provide a discussion on nonstandard analysis and the space of ultrafunctions and their advantages in the applications of quantum mechanics, particularly, for the Schrödinger equation for a Hamiltonian with the Dirac delta potential.