Understanding Kronig-Penney Model in Solid-State Physics

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Homework Statement


This question refers to Kittel's solid-state physics book.

On this page, in the section about the "Kronig-Penney Model in Reciprocal Space", I do not understand why the sum over s is from 0 to 1/a. What if a is 2?

Also, how do they know that "the boundary conditions are periodic over a ring of unit length"?

Homework Equations


The Attempt at a Solution

 
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Then you only sum over zero.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.

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