An outline of Quantum Mechanics in tempered distributions spaces: Schwartz Linear Algebra

Schwartz Linear Algebra extends the operational toolbox of Laurent Schwartz’s Distribution Theory, a celebrated cornerstone of modern analysis, to provide a rigorous and manageable mathematical structure for addressing foundational problems of quantum mechanics in infinite-dimensional spaces. Schwartz linear algebra is motivated by the need to formalize and enhance the mathematical underpinnings of quantum mechanics, particularly the Dirac formalism, while also finding applications in Relativistic quantum mechanics and electromagnetic theory. Our survey explores the origins, key concepts, and implications of Schwartz Linear Algebra, focusing on its theoretical foundations and practical utility.