一维有限深势阱中Ehrenfest定理的证明与验证研究

Research on the proof and verification of Ehrenfest theorem in one dimensional finite deep potential well

利用薛定谔方程及其共轭方程一维有限深势阱中Ehrenfest定理进行了证明,并利用一维无限深势阱的基态和第一激发态波函数给出了体系任意时刻的波函数,在此基础上验证了Ehrenfest定理。结果表明:与应用Ehrenfest定理的两种形式在一维方形势阱中成立。

It is proved by using Schrodinger equation and its conjugate equation Ehrenfest theorem in one-dimensional finite deep potential well,The wave functions of the system at any time are given by using the wave functions of the ground state and first excited state of the one-dimensional infinite potential well,On this basis,Ehrenfest theorem is verified.The results show that the two forms of Ehrenfest’s theorem are valid in one dimensional suquare well.