# Deriving the needed wavefunction transformation for gauge symmetry?

1. Apr 3, 2010

### quarky2001

1. The problem statement, all variables and given/known data
Take the Schrodinger 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 $\phi \rightarrow \phi - \frac{\partial F}{\partial t}$

3. 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 $\Psi \rightarrow \Psi\prime$.

2. Apr 4, 2010

### phyzguy

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