Band diagrams of solids

If we have a wave function v(/ that is a solntion to our problem, then it should necessarily fulfill the following equation  

In the hypothesis that there is only one atom g, the corresponding wave function cpg would meet the condition  

If there are N atoms, we can then consider that the function i/ we are looking for is a linear combination of the N discrete solutions, that is to say  

The knowledge of p is directly related to that of all of the 3g, and to that of some conditions that have to be met by (pg  

1) The ag coefficients must be a function of the wave vector kg (the wave vector describes a wave s capability of moving in a given enviroiunent and direction). In the simple case of a sine-wave propagation, we would have for instance  

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