利用Lagrange方程演绎Schrodinger方程的守恒定律  

The Conservation Law of Schrodinger Equation Obtained by Lagrange Equation

作　　者：杨祺 张琦森 郑永刚[1] YANG Qi;ZHANG Qisen;ZHENG Yonggang(School of Physics and Electronic Information,Yunnan Normal University,Kunming Yunnan 650092,China;Shiji Jinyuan School Attached to Yunnan Normal University,Kunming Yunnan 650214,China)

机构地区：[1]云南师范大学物理与电子信息学院,昆明650092 [2]云南师范大学附属世纪金源学校,昆明650214

出　　处：《保山学院学报》2022年第5期51-54,共4页JOURNAL OF BAOSHAN UNIVERSITY

基　　金：国家自然科学基金“耀变体喷流内电子能谱形成和高能辐射机制研究”(项目编号:11873043)。

摘　　要：在相对论量子场论中,可以将Draic方程通过最小作用量原理构造得到。与此类似,使用最小作用量原理也可以构造Schrodinger方程,并且将量子力学波函数比作经典场的话,波动力学的能量、动量、角动量守恒可以完全看成是经典场的结果。通过构造Schrodinger方程的Lagrange函数的方法,利用最小作用量原理来得到量子力学的守恒定律的微分形式——动量、能量、角动量的守恒方程,这些守恒定律分别对应空间、时间和转动的不变性,这一结果并不违背我们熟知的守恒量算符在Hilbert空间的内积的结果,并通过U(1)对称性可以得到概率流守恒。In relativistic quantum field theory,the Draic equation can be constructed by the principle of minimum action.Similarly,Schrodinger equation can be constructed by using the principle of minimum action,and the conservation of energy,momentum and angular momentum of quantum mechanics can be completely regarded as the result of the classical field if the wave function of quantum mechanics is compared to the classical field.This paper introduces the method of constructing the Lagrange function of Schrodinger equation,and uses the principle of minimum action to obtain the differential equation of conservation law of quantum mechanics–the conservation form of momentum,energy and angular momentum,which correspond to invariance of space,time,and rotation.This result does not violate the inner product of conservation operator in Hilbert space.The conservation of probabilistic flow is obtained by U(1)symmetry.

关 键 词：LAGRANGE方程 SCHRODINGER方程 NOETHER定理 守恒定律 

分 类 号：O4[理学—物理]