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 SCHR?DINGER EQUATION
王雯宇 1程茜 1梁淇玮 1杨琳朔1
作者信息
- 1. 北京工业大学物理与光电工程学院,北京 100124
- 折叠
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.
Abstract
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 evolu-tion solution and presents two derivation methods.Then the paper further generalizes to ob-tain more non-series analytical solutions for time evolution oscillator,and finds the recursive relation to obtain these analytical solutions.Finally,the educational significance and applica-tions of these analytical solutions are discussed.
关键词
薛定谔方程/谐振子/含时演化/解析解Key words
Schrödinger equation/harmonic oscillator/time evolution/analytical solution引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据