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For a charged quantum particle, say, an electron or a quark, how in the particle's wavefunction is the electric charge represented? Is it truly possible to represent electric charge using the wave mechanics formulation of quantum mechanics, or is that something only matrix mechanics can satisfy? And does the same apply for other quantum properties, such as color charge or spin?

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You can construct the conserved current from the wave function for the wave equation, for example, for the Dirac equation. The zeroth component of the current is the charge density (I am cutting some corners here).

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