Motivations and origins of Schwartz Linear Algebra in Quantum Mechanics

David Carfì ()

Journal of Mathematical Economics and Finance, 2016, vol. 2, issue 2, 67-76

Abstract: We propose by Schwartz Linear Algebra a significant development of Laurent Schwartz Distribution Theory The study is conducted by following the natu ral and straightforward way of Weak Duality among topological vector spaces aiming at the construction of a feasible rigorous quite elementary and manageable frame work for Quantum Mechanics It turns out that distribution spaces reveal themselves an environment more capable to help in Quantum Mechanics than previously thought The goal of the research introduced here consists in showing that the most natural state spaces of a quantum system in the infinite dimensional case are indeed dis tribution spaces Moreover we show new natural and straightforward mathematical structures that reproduce very closely several physical objects and many operational procedures required in Quantum Mechanics systematizing the algorithms and nota tions of Dirac Calculus in such a way that it becomes a more versatile and more powerful tool than we are used to think of

Date: 2016
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