Quantum derivatives and the Schrödinger equation
type: Item
instance of: scholarly article
title: Quantum derivatives and the Schrödinger equation
zbMATH Open document ID: 1053.81027
DOI: 10.1016/S0960-0779(03)00339-4
author: Fayçal Ben Adda
author: Jacky Cresson
published in: Chaos, Solitons and Fractals
publication date: 2004-08-19T00:00:00Z
review text: The authors justify the results of [\textit{L. Nottale} Astronom Asrophys. 327, 867--889 (1997), Chaos Solutions Fractals 10, No. 2--3, 459--468 (1999; Zbl 0997.81526)]. The authors give a precise definition of scale derivatives by means of quantum derivatives for non-differentiable functions. Note that these derivatives are not derivations on the set of continuous functions, since they do not satisfy the Leibniz rule. It is shown that scale derivation is an extension of ordinary differentiation. It is derived the Schrödinger equation via the scale-relativity principle and Newton's fundamental equation of dynamics.
reviewed by: Farruh Mukhamedov
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 2093082
zbMATH Keywords: quantum derevative
zbMATH Keywords: scale derivarive
zbMATH Keywords: non-differentiable function
zbMATH Keywords: the Schrödinger equation
Wikidata QID: Q29393907
MaRDI profile type: Publication
cites work: About non-differentiable functions
cites work: Scale relativity theory for one-dimensional non-differentiable manifolds
cites work: Q5569065
cites work: Q5732712
cites work: Q4274291
cites work: Q4242532
cites work: The scale-relativity program
cites work: Q2723195
description: scientific article; zbMATH DE number 2093082