Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 34E / a / Solution

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For a particle of charge $-e$, the changes $A\mapsto A+\nabla f$ and $\phi\mapsto\phi-\partial_t f$ leave the minimally coupled Schrödinger equation invariant when $\psi\mapsto e^{-ief/\hbar}\psi$.


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 Incoming links: Gauge covariance of the Schrödinger equation