The underlying Brownian motion of nonrelativistic quantum mechanics

Foundations of Physics 11 (9-10):653-678 (1981)

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Abstract
Nonrelativistic quantum mechanics can be derived from real Markov diffusion processes by extending the concept of probability measure to the complex domain. This appears as the only natural way of introducing formally classical probabilistic concepts into quantum mechanics. To every quantum state there is a corresponding complex Fokker-Planck equation. The particle drift is conditioned by an auxiliary equation which is obtained through stochastic energy conservation; the logarithmic transform of this equation is the Schrödinger equation. To every quantum mechanical operator there is a stochastic process; the replacement of operators by processes leads to all the well-known results of quantum mechanics, using stochastic calculus instead of formal quantum rules. Comparison is made with the classical stochastic approaches and the Feynman path integral formulation
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DOI 10.1007/BF00726943
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The Physical Principles of the Quantum Theory.Werner Heisenberg - 1930 - Chicago: Ill., The University of Chicago Press.

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