Klein-Gordon方程和时间相关Schrödinger方程的推导形成经典波函数

Journal of Karary University for Engineering and Science Pub Date : 2022-10-14 DOI:10.54388/jkues.v2i3.131

Mobarak Tag, Wail Hessen, Adil Elrayah, Emad Eldin Medani

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引用次数: 0

摘要

在本研究中，Klein-Gordon方程和时变薛定谔方程都是直接由De Broglie (\ λ =h/p)导出的。此外，利用经典波函数和相对论总能量关系[[hw] = [(h^2 k^2)/2m] + V]两个方程，得到了Klein-Gordon方程的新公式。在此基础上，导出了三维空间中新的时变薛定谔方程(TDSE)。因此，前面的结果对应于使用两个方程(即爱因斯坦能量和牛顿力学第二定律)计算的三维(TDSE)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Derivation of both Klein-Gordon equation and Time Dependent Schrödinger Equation form classical wave function

In this study, both the Klein-Gordon equation and time-dependent Schrodinger equation are directly derived from De Broglie's (\lamda=h/p). Besides that, a new formula of the Klein-Gordon equation was obtained by using two equations, i.e., the classical wave function and relativistic total energy relation [[hw] = [(h^2 k^2)/2m] + V]. Moreover, a new equation of time-dependent Schrodinger (TDSE) in three-dimension 3D was derived and evidently obtained. Thus, the previous result corresponds to (TDSE) in 3D calculated using two equations, (i.e., Einstein energy and Newton's second law of mechanics).

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Journal of Karary University for Engineering and Science

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