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 (wikipedia)