Duplex numbers, diffusion systems, and generalized quantum mechanics
Mathematical Physics
2012-01-17 v1 math.MP
Quantum Physics
Abstract
We show that the relation between the Schr\"odinger equation and diffusion processes has an algebraic nature and can be revealed via the structure of "duplex numbers." This helps one to clarify that quantum mechanics cannot be reduced to diffusion theory. Also, a generalized version of quantum mechanics where is replaced by a normed algebra with a unit is proposed.
Cite
@article{arxiv.1201.3069,
title = {Duplex numbers, diffusion systems, and generalized quantum mechanics},
author = {Jerzy Kocik},
journal= {arXiv preprint arXiv:1201.3069},
year = {2012}
}
Comments
10 pages. Term "hyperbolic numbers" would be a better choice than "duplex numbers" used in the article. The formalism presented became known as "hyperbolic quantum mechanics"