2 Conservation of Current

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On the left is plotted the square of the wave function for a state (at 12.4 eV) near the top of the 3rd band. It is nearly a standing wave, as is appropriate for an energy near the edge of the band. Copy graph this, show the phase of psi and steal data to superpose the second graph on the first. Remember that the discontinuities in the phase graph are additions (or subtractions) of 2*pi to keep the function within the range -pi to pi.

Now observe that the rapid variations in phase (NOT the discontinuities which are artifacts) occur at the z-values for which the wave function squared is a minimum. Writing the wave function as (amplitude)*exp(i*phase) you should be able to understand the reason for this by requiring that the particle current be independent of position.