Infinitesimal and Infinite Numbers as an Approach to Quantum Mechanics

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.

arXiv comment18 pages, 2 figures

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Cited by in corpus (2)

• Halos and undecidability of tensor stable positive maps
• A characterization of singular Schrödinger operators on the half-line