Mathematical formalisms for quantum mechanics are distinguished from pre-1900s physics theories by the use of abstract mathematical structures such as infinite-dimensional Hilbert spaces.
Notes on verification
Multiple authoritative academic sources (arXiv papers) and specialized quantum computing resources confirm the use of infinite-dimensional Hilbert spaces in quantum mechanics. Von Neumann's foundational work is well-documented. The distinction from classical mechanics' finite-dimensional phase spaces is corroborated across multiple independent sources.
Sources
- Mathematical formulation of quantum mechanics (en.wikipedia.org)
- https://arxiv.org/pdf/quant-ph/0506184 (arxiv.org)
- https://plato.stanford.edu/entries/qt-nvd/ (plato.stanford.edu)
- https://arxiv.org/pdf/2112.05619 (arxiv.org)
- https://arxiv.org/pdf/1508.06951 (arxiv.org)
- https://arxiv.org/pdf/2305.01560 (arxiv.org)
- https://www.math.ru.nl/~landsman/HSQM2006.pdf (math.ru.nl)