What are the mathematical foundations of quantum mechanics?
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The mathematical foundations of quantum mechanics involve the development of the theory and its key concepts. Quantum mechanics is a mathematical formalism that accurately predicts observable physical phenomena, but it has many puzzling properties. The theory began with the introduction of Planck's constant in 1900, leading to the "old" quantum theory and Bohr's model of the atom. It further evolved with the introduction of matter waves in 1924 and the establishment of the complete fundamental structure of quantum mechanics by 1928. This included the Schrödinger equation, the equivalence to Heisenberg's matrix mechanics, and the relativistic Dirac equation. The theory remains largely unchanged today and has fueled the technological revolution. The interpretation of quantum mechanics remains controversial, with various theories proposed to explain its puzzling features.
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| Papers (5) | Insight |
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| The mathematical foundations of quantum mechanics can be derived from the model of the elastic continuum by Augustin Cauchy, using the Hamilton quaternion algebra. | |
| The paper discusses some important mathematical results in quantum foundations, including Bell's theorem, the Kochen-Specker theorem, and the PBR theorem. | |
| The mathematical foundations of quantum mechanics involve the use of quantum amplitudes and basis vectors to describe the quantum state of a system. | |
| The mathematical foundations of quantum mechanics were established by von Neumann in his book, which introduced the concept of the density matrix and proved the absence of hidden parameters in quantum mechanics. | |
| The mathematical foundations of quantum mechanics include the Schrödinger equation, Heisenberg's matrix mechanics, and the relativistic Dirac equation. |
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