Abstract
It is shown that the Hilbert space formalism of quantum mechanics can be derived as a corrected form of probability theory. These constructions yield the Schrödinger equation for a particle in an electromagnetic field and exhibit a relationship of this equation to Markov processes. The operator formalism for expectation values is shown to be related to anL 2 representation of marginal distributions and a relationship of the commutation rules for canonically conjugate observables to a topological relationship of two manifolds is indicated.
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Collins, R.E. Quantum theory: A Hilbert space formalism for probability theory. Found Phys 7, 475–494 (1977). https://doi.org/10.1007/BF00708864
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DOI: https://doi.org/10.1007/BF00708864