Homework Help: Quantum Mechanics Question

WHat is the time dependence of each term in your sum? Consider shifting the time t by [tex] 2 \pi / \omega [/tex] and see what happens.

 

It has been a while for me, but I believe nrged is saying to apply the time-evolution operator,

e^(iHt)
or maybe it was
e^(-iHt)

Have the covered this concept in your class?

 

First things first. What is the time dependence of the total wavefunction? Psi is a linear combination of the eigenstates of the Hamiltonian, right? What is the time dependence of each eigenstate? What i sthe time dependence of the total wavefunction? Can you writ edown the total wavefunction, showing explicitly its time dependence?

Then you should simply replace t by t+2 pi/omega in you expression and you should see that the total wavefunction remains unchanged. That's what I meant by "shifting the time".

 

Well, it could be done this way, yes. But I had something simpler in mind...see my previous post.

 

Okay. I didn't see the necessary e^iwt factors explicitly in the original description, but perhaps they are in Shomy's textbook or class notes description of the H.O. wavefunctions.

 

That's what I wanted him/her to realize: that there are factors [tex] e^{-iE_n t/\hbar} [/tex]