Structure of Quantum Mechanics
K.A. Lebedev, Евгений Николаевич Тумаев
Interest in quantum mechanics is growing in connection with new experiments with quantum particles and a deeper knowledge of nano- and subatomic principles. The practical use of quantum mechanic methods goes in parallel with the constant rethinking of its foundations, its ideological and epistemological role. A rigorous exposition of the mathematical foundations of quantum mechanics in abstract-Hilbert spaces was given in the book of J. Von Neumann in 1933. It is the first and only experiment that has been brought to the end, the presentation of the apparatus of quantum mechanics with the sequence and rigor which usually presented in a purely mathematical theory. Later in 1949 the group of French mathematicians under the pseudonym N. Bourbaki introduced the concept of "mathematical structure" into mathematics. To date, there is no narration of quantum mechanics, where mathematical rigor is combined with the concept of "mathematical structure". In the framework of the approach formulated by the group of N. Burbaki, quantum mechanics is a composite structure consisting of three simple mathematical structures: the Hilbert space of complex-valued vectors, the space of linear self-adjoint operators and the structure of classical mechanics are showed in this article.
Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation•Jun 26, 2020•1 citation