一维均匀势场中含时薛定谔方程的求解  

Solution of Schr dinger equation in a 1D homogeneous field

作　　者：任喜军 刘祥瑞 REN Xi-jun;LIU Xiang-rui(Physics Department,School of Physics and Electronics,Henan University,Kaifeng,Henan 475004,China)

机构地区：[1]河南大学物理与电子学院物理学系,河南开封475004

出　　处：《大学物理》2023年第7期3-5,52,共4页College Physics

基　　金：河南大学明德计划资助。

摘　　要：本文详细讨论了一维均匀势场中含时薛定谔方程的求解.求解的思想是以均匀势场中经典粒子的运动作为参考,从经典粒子的运动轨迹出发,构建出量子情形下描述粒子运动的高斯波包形式的演化波函数,进而借助含时薛定谔方程确定波函数的具体形式.在上述思想指导下,推导得出了坐标表象和动量表象下均匀势场内一维粒子的传播子函数.同时,作为比较,狄拉克态矢量符号提供了另一种得到上述传播子函数的途径.The solution of time dependent Schr dinger equation in a one-dimensional homogeneous field is carried out in detail.The idea is,based on the classical trajectory of a classical particle in the homogenous filed,the time dependent wave function can be constructed from this trajectory with a phase factor function which is determined by solving the Schr dinger equation.Guided by this idea,the propagator function of homogeneous field is obtained for both position representation and momentum representation.Meanwhile,Dirac notation for state vectors is employed to obtain the above results for comparison.

关 键 词：薛定谔方程 坐标表象 动量表象 狄拉克符号 传播子函数 

分 类 号：O413[理学—理论物理]