Quantum derivatives and the Schrödinger equation
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.
- Publication:
-
Chaos Solitons and Fractals
- Pub Date:
- March 2004
- DOI:
- 10.1016/S0960-0779(03)00339-4
- Bibcode:
- 2004CSF....19.1323B