G01

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**1. Suppose a constant potential energy,Vo, independent of x and t is added to a particle's potential energy. Show that this adds a time-dependent phase factor, [tex] e^{-iV_ot/\hbar}[/tex]**

Right now I'm completely lost. Here's what I think so far:

**2.**

[tex]i\hbar\frac{d\Psi}{dt} = \frac{-\hbar^2}{2m}\frac{d^2\Psi}{dx^2} + V(x)\Psi[/tex]

[tex]i\hbar\frac{d\Psi}{dt} = \frac{-\hbar^2}{2m}\frac{d^2\Psi}{dx^2} + V(x)\Psi[/tex]

As I said, I'm lost(Maybe I'm just to tired.) I added in the constant Potential Energy Term and that changes the Shrodinger Eq. like so:

**3.[tex]i\hbar\frac{d\Psi}{dt} = \frac{-\hbar^2}{2m}\frac{d^2\Psi}{dx^2} + V(x)\Psi + V_o\Psi[/tex]**

Now I'm stuck. As I write this I'm thinking about moving the constant term to the time side, separating ans solving the time side, since I know the answer is Time-dependent. Is this the right way to proceed? I'm not asking for a solution to the problem, just a hint about where to go. For reference this is problem 1.8 out of Griffith. Thank-you for any hints you can give me. I really appreciate it. If I need to show more work tell me and If I have accomplished anything else I will post it.

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