Quantum mechanics is the square root of a stochastic process

2012/01/24 by Marco Frasca, Frasca, Marco · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1201.5091

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

openalex publication_date 2012/01/24 · arxiv created 2012/01/29 · arxiv updated 2012/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. Schrödinger equation is immediately derived without further assumptions using Itō 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.

Citations

• Dynamical Theories of Brownian Motion

Cited by

• Quantum Systems as Indivisible Stochastic Processes

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