Maupertuis原理与薛定谔方程的建立  

MAUPERTUIS PRINCIPLE AND ESTABLISHMENT OF SCHRÖDINGER EQUATION

作　　者：张成园 丁勇[1] 许广智[1] 王军平 李永庆[1] ZHANG Chengyuan;DING Yong;XU Guangzhi;WANG Junping;LI Yongqing(Department of Physics,Liaoning University,Shenyang,Liaoning 110036)

机构地区：[1]辽宁大学物理学院,辽宁沈阳110036

出　　处：《物理与工程》2025年第1期63-65,78,共4页Physics and Engineering

基　　金：辽宁省普通高等教育本科教学改革研究项目(2022-10140-11);辽宁省研究生教育教学改革研究项目(LNYJG2023001,LNYJG2022010);辽宁大学研究生优质在线课程建设与教学模式综合改革研究项目(YJG202201014,YJG202302096);辽宁大学第二批课程思政示范课程(100);2022年辽宁大学研究生“课程思政”示范课程(25);辽宁大学本科教学改革研究项目(JG2021PTXM004,JG2022BYLW004)。

摘　　要：薛定谔方程是量子力学的基本方程,主要讨论量子态随时间的演化以及具体情况下求解波函数的问题,其地位与经典力学中的牛顿方程相当。本文基于文献《关于量子力学中引入波粒二象性的教学尝试》,进一步通过Maupertuis原理建立薛定谔方程。通过对比几种典型建立薛定谔方程的教学方法,进一步突出本文提出方法的特点,从而有助于学生将新旧知识进行有机融合,更容易接受和理解量子力学的基本方程,增强学生对知识的迁移能力,激发学生的创造性思维。The Schrödinger equation is the fundamental equation of quantum mechanics,primarily discussing the evolution of quantum states over time and solving the wave function under specific conditions.Its position is equivalent to that of Newton's equation in classical mechanics.Based on the literature“Teaching Attempts to Introduce Wave-Particle Duality in Quantum Mechanics,”this paper further establishes the Schrödinger equation through the Maupertuis principle.By comparing several typical teaching methods for establishing the Schrödinger equation,the characteristics of the method proposed in this paper are further highlighted,which helps students to integrate new and old knowledge organically,more easily accept and understand the basic equations of quantum mechanics,enhance studentsability to transfer knowledge,and stimulate studentscreative thinking.

关 键 词：Maupertuis原理 薛定谔方程 哈密顿雅可比方程 

分 类 号：O413.1[理学—理论物理]