Deriving the needed wavefunction transformation for gauge symmetry?

  • Thread starter quarky2001
  • Start date
  • #1
34
0

Homework Statement


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

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

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


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 [itex] \Psi \rightarrow \Psi\prime [/itex].
 

Answers and Replies

  • #2
phyzguy
Science Advisor
4,790
1,744
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'.
 

Related Threads on Deriving the needed wavefunction transformation for gauge symmetry?

Replies
1
Views
824
Replies
0
Views
6K
  • Last Post
Replies
0
Views
1K
Replies
1
Views
646
Replies
0
Views
677
Replies
2
Views
310
Replies
4
Views
772
  • Last Post
Replies
10
Views
761
Replies
7
Views
412
  • Last Post
Replies
0
Views
1K
Top