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Duplex numbers, diffusion systems, and generalized quantum mechanics. (English) Zbl 0938.81003

Summary: The author shows that the relation between the Schrödinger equation and diffusion processes has an algebraic nature and can be revealed via the structure of “duplex numbers”. This helps to clarify that quantum mechanics cannot be reduced to diffusion theory. Also, a generalized version of quantum mechancis where \(\mathbb{C}\) is replaced by a normed algebra with a unit is proposed.

MSC:

81P05 General and philosophical questions in quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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