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Deriving the needed wavefunction transformation for gauge symmetry?

  1. Apr 3, 2010 #1
    1. The problem statement, all variables and given/known data
    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]

    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 [itex] \Psi \rightarrow \Psi\prime [/itex].
  2. jcsd
  3. Apr 4, 2010 #2


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    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'.
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