Quantum mechanics is the square root of a stochastic process

Details Quantum mechanics is the square root of a stochastic process Quantum mechanics is the square root of a stochastic process

2012-01-24

arxiv.org/abs/1201.5091v2

Physics

Mathematical Physics

4 pages, no figure. Extended mathematics to fix a problem in the definition of Ito integrals

Scientific paper

We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued stochastic process is involved. Schr\"odinger equation is immediately derived without further assumptions using It\=o integrals that are properly generalized. Fluctuations in space arise from a Brownian motion and the combined effect of a stochastic process with a symmetric Bernoulli distribution typical of tossing a coin.

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