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Suppose that the electron inside a material is subjected to a periodic potential with spatial periodicity a (i.e., lattice parameter). Show that under these conditions

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Suppose that the electron inside a material is subjected to a periodic potential with spatial periodicity a (i.e., lattice parameter). Show that under these conditions the value of the wavefunction at any point x in real space must be equal to its value at (x+na) where n is the an integer (with the limitation on n that x +na must lie within the periodic potential if it is of finite extent)

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