OBTAINING MACROMECHANICAL VALUES USING QUANTUM-MECHANICAL DIFFERENTIAL EQUATIONS

I. Popov
{"title":"OBTAINING MACROMECHANICAL VALUES USING QUANTUM-MECHANICAL DIFFERENTIAL EQUATIONS","authors":"I. Popov","doi":"10.31040/2222-8349-2022-0-3-12-15","DOIUrl":null,"url":null,"abstract":"The wave function Ψ satisfies the Schrödinger equation for a free particle. Formally, the Schrödinger equation generates the magnitude of mechanical motion of the zero order 0 p = mv 0 (in the sense that it is contained in the Schrödinger equation. Comparison of the wave function Ψ and its gradient implies a formal analogue of the Schrödinger equation, which generates the magnitude of mechanical motion of the first order 1 p = mv 1. From the comparison of the wave function and its time derivative yields a formal analogue of the Schrödinger equation, which generates the magnitude of mechanical motion of the second order 2 p = mv 2/2!. The values of mechanical motion of the zero, first, and second orders are known.Obviously, other formal analogs of the Schrödinger equation can generate mechanical motion of other orders.The aim of the work is to establish such quantities and related regularities that may be of interest, which makes the study relevant. hovering. Then the spatial derivatives will be one-dimensional. The magnitude of the mechanical movement of the third order is 3 p = mv 3/3!. This value is Umov's integral vector for kinetic energy. The magnitude of the mechanical movement minus the first order -1 p = mv -1 is a reverse impulse. The meaning of this quantity and its relevance is established by the theorem: in a hy- drogen-like atom, the quantity m v-1 is quantized. A fixed (unchanged) quantum is a quantity m v-1 correspond- e e 0 ing to the basic energy level. Almost all of the results obtained were a consequence of the use of quantum mechanical differential equations, however, the results themselves are predominantly macromechanical. The quantities of mechanical motion of various orders are generated by formal analogs of the Schrödinger equation. In all formal analogs of the Schrödinger equation, the orders of the partial derivatives differ by one. For quantities of motion with a positive degree of velocity, the order of the temporal derivatives is higher than that of the spatial ones. For quantities with a negative degree, the order of spatial derivatives is higher.","PeriodicalId":220280,"journal":{"name":"Izvestia Ufimskogo Nauchnogo Tsentra RAN","volume":"330 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestia Ufimskogo Nauchnogo Tsentra RAN","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31040/2222-8349-2022-0-3-12-15","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

The wave function Ψ satisfies the Schrödinger equation for a free particle. Formally, the Schrödinger equation generates the magnitude of mechanical motion of the zero order 0 p = mv 0 (in the sense that it is contained in the Schrödinger equation. Comparison of the wave function Ψ and its gradient implies a formal analogue of the Schrödinger equation, which generates the magnitude of mechanical motion of the first order 1 p = mv 1. From the comparison of the wave function and its time derivative yields a formal analogue of the Schrödinger equation, which generates the magnitude of mechanical motion of the second order 2 p = mv 2/2!. The values of mechanical motion of the zero, first, and second orders are known.Obviously, other formal analogs of the Schrödinger equation can generate mechanical motion of other orders.The aim of the work is to establish such quantities and related regularities that may be of interest, which makes the study relevant. hovering. Then the spatial derivatives will be one-dimensional. The magnitude of the mechanical movement of the third order is 3 p = mv 3/3!. This value is Umov's integral vector for kinetic energy. The magnitude of the mechanical movement minus the first order -1 p = mv -1 is a reverse impulse. The meaning of this quantity and its relevance is established by the theorem: in a hy- drogen-like atom, the quantity m v-1 is quantized. A fixed (unchanged) quantum is a quantity m v-1 correspond- e e 0 ing to the basic energy level. Almost all of the results obtained were a consequence of the use of quantum mechanical differential equations, however, the results themselves are predominantly macromechanical. The quantities of mechanical motion of various orders are generated by formal analogs of the Schrödinger equation. In all formal analogs of the Schrödinger equation, the orders of the partial derivatives differ by one. For quantities of motion with a positive degree of velocity, the order of the temporal derivatives is higher than that of the spatial ones. For quantities with a negative degree, the order of spatial derivatives is higher.
利用量子力学微分方程获得宏观力学值
波函数Ψ满足自由粒子的Schrödinger方程。形式上,Schrödinger方程产生了0阶机械运动的大小p = mv 0(从这个意义上说,它包含在Schrödinger方程中。波函数Ψ与其梯度的比较意味着Schrödinger方程的形式模拟,它产生一阶机械运动的大小1 p = mv 1。从波函数和它的时间导数的比较中得到Schrödinger方程的形式模拟,它产生了二阶机械运动的大小2 p = mv 2/2!机械运动的零、一、二阶的值是已知的。显然,Schrödinger方程的其他形式类比可以产生其他阶次的机械运动。这项工作的目的是建立可能感兴趣的数量和相关规律,这使得研究具有相关性。盘旋。那么空间导数就是一维的。三阶机械运动的大小是3p = mv 3/3!这个值是动能的乌莫夫积分向量。机械运动的大小减去一阶-1 p = mv -1是一个逆脉冲。这个量的意义和它的相关性是由以下定理建立的:在类氢原子中,量m v-1是量子化的。一个固定的(不变的)量子是与基本能级对应的量m v-1。几乎所有得到的结果都是使用量子力学微分方程的结果,然而,结果本身主要是宏观力学的。不同阶次的机械运动量由Schrödinger方程的形式类比产生。在所有类似Schrödinger方程的形式中,偏导数的阶数相差1。对于速度为正的运动量,时间导数的阶数高于空间导数的阶数。对于具有负次的量,空间导数的阶数较高。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信