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Mind you, the wave function transform is just one part of the prescription. The other part is the transform of the electromagnetic four-potential. The latter enters into the generalized momentum. Remember, a gauge transform produces a physically equivalent solution. Do you really dispute this statement?I don't think that prescription preserves expectation values, in general. Consider:

[tex]

\langle \psi | \hat{p} |\psi \rangle =\int dx \; \langle \psi | x \rangle \langle x | \hat{p} |\psi \rangle = \int dx \; \psi^{*}(x) \left( -i \frac{\partial}{\partial x} \right) \psi(x)

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then under the transformation

[tex]

\rightarrow \int dx \; \psi'^{*}(x) \left( -i \frac{\partial}{\partial x} \right) \psi'(x) = \int dx \; \psi^{*}(x)e^{-i\theta(x)} \left( -i \frac{\partial}{\partial x} \right) e^{i \theta(x)}\psi(x) \neq \int dx \; \psi^{*}(x) \left( -i \frac{\partial}{\partial x} \right) \psi(x)

[/tex]

How is that accounted for?