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Quantum derivatives and the Schrödinger equation |
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| Authors: | Fayal Ben Adda Jacky Cresson |
| Institution: | a Mathematical Sciences Department, Hail Community College, King Fahd University of Petroleum and Minerals, P.O. Box 2440, 44 Avenue Bartholdi, 72000 le Mans, Hail, Saudi Arabia b Equipe de Mathématiques de Besançon, Université de Franche-Comté, CNRS-UMR 6623, 16, route de Gray, 25030, Besançon Cedex, France |
| Abstract: | We define a scale derivative for non-differentiable functions. It is constructed via quantum derivatives which take into account non-differentiability and the existence of a minimal resolution for mean representation. This justify heuristic computations made by Nottale in scale-relativity. In particular, the Schrödinger equation is derived via the scale-relativity principle and Newton’s fundamental equation of dynamics. |
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