Space-Time Geodesics and the Derivation of Schr\"odinger's equation

Faycal Ben Adda

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arXiv · 1805.03509

Space-Time Geodesics and the Derivation of Schr\"odinger's equation

Faycal Ben Adda

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Abstract

Using the essence of Feynman's path integral and the space-time geodesics, an infinity of differentiable paths that follow the geometry of a continuous geodesic are constructed, and a wave function is associated to each path as a probability amplitude identical to the Feynman's probability amplitude for each path. We prove that each probability amplitude obeys to the Schr\"odinger's equation for a non relativistic physical system moving in a time independent potential, starting from the Jacobi-Hamilton equation.

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Faycal Ben Adda. 2018-05-04. Space-Time Geodesics and the Derivation of Schr\"odinger's equation. https://arxiv.org/abs/1805.03509

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