The Harmonic Oscillator in the Framework of Scale Relativity

Quantum Fest 2016 International Conference on Quantum Phenomena, Quantum Control and Quantum Optics

Bonilla, M.^1 ; Rosas-Ortiz, O.^1

Physics Department, Cinvestav, A.P. 14-740, México City

07000, Mexico^1

关键词: Dinger equation;    Harmonic oscillator potential;    Harmonic oscillators;    Nonlinear differential equation;    Physical systems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/839/1/012009/pdf
DOI  :  10.1088/1742-6596/839/1/012009

来源: IOP

【 摘 要 】

The dynamical law obeyed by the one-dimensional physical systems in the scale relativity approach is reduced to a Riccati nonlinear differential equation. Applied to the harmonic oscillator potential, we show that such an approach permits the calculation of the solutions of the scale relativity problem in terms of the well known solutions of the Schrödinger equation for the harmonic oscillator.