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## Main Question or Discussion Point

I read some derivations of current density from the quantum equations of motion (like Scrödinger's and Klein-Gordon's). They derive an equation with the same form as continuity equation:

div(A)+dB/dt=0

Then they conclude that A=current density and B=density.

However there are non-zero vector fields that have zero divergence, so we could add any of them to A and the continuity equation would still be true. How can we know that A is the true expression for current density?

div(A)+dB/dt=0

Then they conclude that A=current density and B=density.

However there are non-zero vector fields that have zero divergence, so we could add any of them to A and the continuity equation would still be true. How can we know that A is the true expression for current density?

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