Motivations and origins of Schwartz Linear Algebra in Quantum Mechanics
Motivations and origins of Schwartz Linear Algebra in Quantum Mechanics

Summary/Abstract: We propose, by Schwartz Linear Algebra, a significant development of Laurent Schwartz Distribution Theory. The study is conducted by following the( natural and straight forward) 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 infinite dimensional case, are indeed distribution spaces. Moreover, we show new, natural and straight forward mathematical structures that reproduce very closely several physical objects and many operational procedures required in Quantum Mechanics, systematizing the algorithms and notations of Dirac Calculus, in such away that it becomes a more versatile and more powerful tool, than we are used to think of.

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