An Example Polyacetylene with Uniform Bond Lengths

For noncyclic, one-dimensional systems, then, eigenfunctions have the form 

Just as was tme for cyclic cases, we can approximate this Bloch functional form with a Bloch sum  

In chemistry, it is Bloch sums that are normally used. 

Two- or three-dimensional periodic systems can be treated similarly, with separate k vectors for each of the independent translational directions. 

Q 15-7 An Example Polyacetylene with Uniform Bond Lengths 

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