Infinitesimal and Infinite Numbers as an Approach to Quantum Mechanics
Mathematical Physics
2019-05-06 v3 math.MP
Quantum Physics
Abstract
Non-Archimedean mathematics is an approach based on fields which 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 paper, we provide a discussion of the space of ultrafunctions and its advantages in the applications of quantum mechanics, particularly for the Schr\"{o}dinger equation for a Hamiltonian with the delta function potential.
Keywords
Cite
@article{arxiv.1901.10945,
title = {Infinitesimal and Infinite Numbers as an Approach to Quantum Mechanics},
author = {Vieri Benci and Lorenzo Luperi Baglini and Kyrylo Simonov},
journal= {arXiv preprint arXiv:1901.10945},
year = {2019}
}
Comments
18 pages, 2 figures