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.