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arXiv · 1901.10945

Infinitesimal and Infinite Numbers as an Approach to Quantum Mechanics

Vieri Benci·Lorenzo Luperi Baglini·Kyrylo Simonov
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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 Schrödinger equation for a Hamiltonian with the delta function potential.

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Vieri Benci, Lorenzo Luperi Baglini, Kyrylo Simonov. 2019-04-26. Infinitesimal and Infinite Numbers as an Approach to Quantum Mechanics. https://doi.org/10.22331/q-2019-05-03-137

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