Duplex numbers, diffusion systems, and generalized quantum mechanics

Details Duplex numbers, diffusion systems, and generalized quantum mechanics Duplex numbers, diffusion systems, and generalized quantum mechanics

2012-01-15

arxiv.org/abs/1201.3069v1

International Journal of Theoretical Physics, Vol. 38 No. 8, 1999 (pp. 2221-30)

Physics

Mathematical Physics

10 pages. Term "hyperbolic numbers" would be a better choice than "duplex numbers" used in the article. The formalism presente

Scientific paper

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 $\C$ is replaced by a normed algebra with a unit is proposed.

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