Floquet-Bloch theorem

The general solution of Eq. (12.6) is given by the Floquet-Bloch theorem, as a sum of products of a spatially periodic amplitudes A( ) and B( ) with oscillating exponential functions... 

This is the parabolic curve shown in Fig. 4.4(a). A linear atomic lattice will provide a periodic rather than a constant potential, i.e. V(x) = V[x + a), where a is the repeat distance of the array. Bloch s theorem, also known as Floquet s theorem, states that possible solutions of the Schrodinger equation with a periodic potential are ... 

The universal structural feature of perfect crystals is their periodicity. An immediate consequence of this periodicity is the Bloch-Floquet theorem stating that the one-electron eigenfunctions are of the form... 

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