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In many textbooks and sites of solid state physics energy levels for the free electron approximation in band calculations are displayed. The result is a collection of many parabolas, each of these parabolas being centered on a site of the reciprocal lattice.

This is not anyway the picture that should emerge from the free electron solution where we should find a single parabola with vertex at k=0.

Can anyone help me explain this discrepancy?

Thanks a lot

This is not anyway the picture that should emerge from the free electron solution where we should find a single parabola with vertex at k=0.

Can anyone help me explain this discrepancy?

Thanks a lot

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