Starting from a quantum state represented by its wave function Ψ(x), satisfying the Schrödinger equation, we determine stochastic processes which provide the same time evolution for the probability densityν(x)=¦Ψ(x)¦2. The transition probabilities of these processes are explicitly built in two circumstances: in the general case, but in an expansion in the time difference, and exactly, but for Gaussian processes. This allows us to discuss the correspondence between quantum states and stochastic processes, which appears not to be one-to-one, but, on the contrary, to associate with the same state an infinity of processes which differ in the fluctuation correlations of the random variable.
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Jaekel, M.T., Pignon, D. Stochastic processes of a quantum state. Int J Theor Phys 24, 557–569 (1985). https://doi.org/10.1007/BF00670464
- Wave Function
- Field Theory
- Time Evolution
- Elementary Particle
- Quantum Field Theory