Abstract
This chapter is entirely devoted to Nelson’s stochastic mechanics, a theory that formally belongs to classical physics, but leads to the same results as quantum mechanics. In this theory, the motion of a particle is viewed as a stochastic process satisfying a version of the Newton equation. Starting with the probability density of this process, one may find the quantum mechanical wave function, i.e, a solution of the Schrödinger equation. Apparently, Fenyes [48] was the first to introduce and study such processes. However, stochastic mechanics became well known only after the publication of papers [110] and [111] by Nelson who developed the theory independently and gave it a natural form. A more detailed review of the history of this question can be found in [27], [110], and [113].
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© 1997 Springer Science+Business Media New York
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Gliklikh, Y. (1997). Mean Derivatives, Nelson’s Stochastic Mechanics, and Quantization. In: Global Analysis in Mathematical Physics. Applied Mathematical Sciences, vol 122. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1866-1_6
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DOI: https://doi.org/10.1007/978-1-4612-1866-1_6
Publisher Name: Springer, New York, NY
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