Deriving the needed wavefunction transformation for gauge symmetry?

[quarky2001]

Homework Statement

Take the Schrödinger equation for a point particle in a field:

$$i\hbar \frac{\partial \Psi}{\partial t} = \frac{1}{2m}(-i\hbar\nabla - q\vec{A})^2\Psi + q\phi\Psi$$

I'm supposed to determine what the transformation for Psi is that corresponds to the gauge transformation $A\rightarrow A +\nabla F$ and $\phi \rightarrow \phi - \frac{\partial F}{\partial t}$

The Attempt at a Solution

I know what the transformation should be, since these transformations are actually derived the other way around in most textbooks, but I have no idea how to work from these transformations to get the necessary operator for $\Psi \rightarrow \Psi\prime$.

 

[phyzguy]

Assume you have a function psi that satisfies the Schrödinger equation with the un-transformed A, phi, then ask what psi' needs to be to satisfy the Schrödinger equation with the transformed A', phi'.