Paper ID 306

Classical Mechanics Theory and Schrödinger's Equation: A Derivation of Relations

JJiancao Li1 & Yanchun Yu2,*

1Chuzhou College, School of Civil and Architectural Engineering, Chuzhou 239000, China

2Northeast Agricultural University School of Water Conservancy and Architecture, Harbin 150000, China

 

*Corresponding author: 15955083483@163.com

 

Abstract

This study examines integrating the Schrödinger equation with classical mechanics using a virtual axis-to-dimensional expansion. One-dimensional material fluctuations are viewed in a two-dimensional plane, explaining the random nature of these fluctuations and their spatial and temporal trajectories. A quantum-consistent force field is proposed, with its strength determined by the Planck constant and inversely proportional to the distance from the stationary point. Newton's second law is applied to establish a second-order linear differential equation for material fluctuations, from which the standard one-dimensional Schrödinger equation is derived, showing their equivalence. The study extends the three-dimensional Schrödinger equation to include external forces and explains quantum phenomena like energy levels and transitions through particle trajectory changes. This approach connects classical mechanics and quantum mechanics, offering a concise and intuitive formulation with clear physical significance.

Keywords: classical mechanics; newton’s second law; quantum mechanics; schrödinger equation; wave function.

 

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