English

Quantum mechanics is the square root of a stochastic process

Mathematical Physics 2012-01-31 v2 math.MP Quantum Physics

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. 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.

Keywords

Cite

@article{arxiv.1201.5091,
  title  = {Quantum mechanics is the square root of a stochastic process},
  author = {Marco Frasca},
  journal= {arXiv preprint arXiv:1201.5091},
  year   = {2012}
}

Comments

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

R2 v1 2026-06-21T20:09:10.404Z