Infinitesimal and Infinite Numbers as an Approach to Quantum Mechanics

Autor:	Benci, Vieri, Baglini, Lorenzo Luperi, Simonov, Kyrylo
Rok vydání:	2019
Předmět:	Mathematical Physics Quantum Physics
Zdroj:	Quantum 3, 137 (2019)
Druh dokumentu:	Working Paper
DOI:	10.22331/q-2019-05-03-137
Popis:	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. Comment: 18 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1901.10945 Zobrazit plný text záznamu View this record from Arxiv