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

Jiancao  Li; Yanchun Yu

doi:10.5614/j.eng.technol.sci.2025.57.5.1

Authors

Jiancao Li Chuzhou College, School of Civil and Architectural Engineering, Chuzhou 239000, China, China
Yanchun Yu
yanchunyu743@gmail.com
Northeast Agricultural University School of Water Conservancy and Architecture, Harbin 150000, China, China

Vol. 57 No. 5 (2025): Vol. 57 No. 5 (2025): October (In Progress)

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Accepted July 28, 2025

Published September 23, 2025

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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.

Li, J. ., & Yu, Y. (2025). Classical Mechanics Theory and Schrödinger’s Equation: A Derivation of Relations. Journal of Engineering and Technological Sciences, 57(5), 573–589. https://doi.org/10.5614/j.eng.technol.sci.2025.57.5.1

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