Scale calculus and the Schrödinger equation | Zendy

Jacky Cresson | Zendy

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Scale calculus and the Schrödinger equation

Author(s) -

Jacky Cresson

Publication year - 2003

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.1618923

Subject(s) - mathematics , time scale calculus , quantization (signal processing) , differential calculus , schrödinger's cat , schrödinger equation , differentiable function , calculus (dental) , mathematical analysis , multivariable calculus , medicine , dentistry , algorithm , control engineering , engineering

We introduce the scale calculus, which generalizes the classical differentialcalculus to non differentiable functions. The new derivative is called thescale difference operator. We also introduce the notions of fractal functions,minimal resolution, and quantum representation of a non differentiablefunction. We then define a scale quantization procedure for classicalLagrangian systems inspired by the Scale relativity theory developped byNottale. We prove that the scale quantization of Newtionian mechanics is a nonlinear Schrodinger equation. Under some specific assumptions, we obtain theclassical linear Schrodinger equation.Comment: 49 page

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