一维谐振子薛定谔方程含时演化非级数解析解  

THE ANALYTICAL NON-SERIES TIME EVOLUTION SOLUTION OF ONE DIMENSIONAL OSCILLATOR SCHRÖDINGER EQUATION

作　　者：王雯宇[1] 程茜 梁淇玮 杨琳朔 WANG Wenyu;CHENG Xi;LIANG Qiwei;YANG Linshuo(School of Physics and Optoelectronic Engineering,Beijing University of Technology,Beijing 100124)

机构地区：[1]北京工业大学物理与光电工程学院,北京100124

出　　处：《物理与工程》2024年第4期98-109,共12页Physics and Engineering

摘　　要：1926年薛定谔找到了一个一维谐振子薛定谔方程含时演化解析解。这个解并不是能量本征态波函数级数求和形式。这可以让我们从新的角度理解量子系统的随时间演化行为。本文主要对该含时演化解析解进行了分析,给出了两种推导方法,然后继续推广得到了更多的含时演化非级数解析解,找到了这些解析解的递推关系,最后讨论了这些解析解的教学意义及应用。In 1926,E.Schrödinger found an analytical solution for the time evolution of the one-dimensional harmonic oscillator Schrödinger Equation.This solution is not in the form of a summation of energy eigenstate wave functions,which provides a new perspective on the time evolution in quantum mechanics.This paper mainly analyzes this analytical time evolution solution and presents two derivation methods.Then the paper further generalizes to obtain more non-series analytical solutions for time evolution oscillator,and finds the recursive relation to obtain these analytical solutions.Finally,the educational significance and applications of these analytical solutions are discussed.

关 键 词：薛定谔方程 谐振子 含时演化 解析解 

分 类 号：O413.1[理学—理论物理]