How Does Adding a Constant Potential Affect Quantum Wave Functions?

[broegger]

I am having trouble with an exercise from Griffiths "Introduction to Quantum Mechanics". The exercise is this:

"Suppose you add a constant $$V_0$$ to the potential energy. In classical mechanics this doesn't change anything, but how about quantum mechanics? Show that the wave function picks up a time-dependent phase factor: $$exp(-iV_0t/\bar{h})$$. What effect does this have on the expectation value of a dynamical variable?"

This is an exercise from the first chapter - the Scrödinger equation has only been introduced briefly and he hasn't really talked about potential energy yet. How am I supposed to do this with the limited knowledge I have?

 

[dextercioby]

What are your ideas??Have you seen the derivation of the $exp(-\frac{1}{i\hbar}Et)$ for the stationary states??If so,u may make an analogy.

Daniel.

 

[da_willem]

I am having trouble with an exercise from Griffiths "Introduction to Quantum Mechanics". The exercise is this:

"Suppose you add a constant $$V_0$$ to the potential energy. In classical mechanics this doesn't change anything, but how about quantum mechanics? Show that the wave function picks up a time-dependent phase factor: $$exp(-iV_0t/\bar{h})$$. What effect does this have on the expectation value of a dynamical variable?"

This is an exercise from the first chapter - the Scrödinger equation has only been introduced briefly and he hasn't really talked about potential energy yet. How am I supposed to do this with the limited knowledge I have?

Well, you have seen the Schrödinger equation which contains the potential V! What happens to the solotution of this equation if you add [itex]V_0[/tex] to V?[/itex]

 

[broegger]

That's the question :)

 

[dextercioby]

We're waiting for your post in which to come up with ideas and maybe some calculations.It is not in the intention of this forum to DO HOMEWORKS.It is still your job...

Daniel.

 

[broegger]

I found out. Pretty simple... Thanks anyway, I'll be needing your help in the future...

I'll sketch my ideas in the future, I'm pretty lazy. Sorry :/