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Then en(-iV)f(r) = £ eni f(r) + l • Vf(r) + - l2V2f(r) +

where we have taken into account that the term in curls is the Taylor series for the function /(r + l). Using Eq. (26), we can get

This is the expression for the envelope function, also called the Schrodinger equation in the Wannier representation.

Suppose that the electron moves in only one band. This means that the external potential is weak enough in order to not induce interband transitions; therefore

We will also consider that the potential varies slowly with the position; that is,

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