From Lagrangian mechanics fractal in space to space fractal Schrödinger’s equation via fractional Taylor’s series

Abstract By considering a coarse-grained space as a space in which the point is not infinitely thin, but rather has a thickness, one can arrive at an equivalence, on the modeling standpoint, between coarse-grained space and fractal space. Then, using fractional analysis (slightly different from the standard formal fractional calculus), one obtains a velocity conversion formula which converts problems in fractal space to problems in fractal time, therefore one can apply the corresponding fractional Lagrangian theory (previously proposed by the author). The corresponding fractal Schrodinger’s equation then appears as a direct consequence of the usual correspondence rules. In this framework, the fractal generalization of the Minkowskian pseudo-geodesic is straightforward.

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