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1. The current and charge densities derived in Section 1.4 are guaranteed to conserve charge provided that V(x, t) is real. Show that particles will be created or absorbed if V is complex. This trick is sometimes used for a source or sink of particles in modelling.

2. Construct a wave function to describe electrons moving in the +x-direction at 10⁵m s^-1 and carrying a current density of -1 A mm^-2.

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