What happens if one adds magnetic flux quanta into a Byers-Yang type system (http://en.wikipedia.org/wiki/Byers-Yang_theorem)?

The wavefunction does not change according to the gauge transformation described in the article.

But what happens to the hamiltonian of such system?

If I am not wrong, then substituting the A = A' + \nabla \chi vector potential into a Pauli equation will produce some new terms, which I think will change the energy...

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