This is basically what became the dominant formulation as of 2020 (and much earlier), and so we just call it the "mathematical formulation of quantum mechanics".
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The Dirac-von Neumann axioms, also known as the axioms of quantum mechanics, provide a formal framework to describe the mathematical structure of quantum mechanics. They were formulated by physicist Paul Dirac and mathematician John von Neumann in the early 20th century and establish the foundation for the theory. The axioms can be summarized as follows: 1. **State Space**: The state of a physical system is described by a vector in a complex Hilbert space.