Tight-binding model answer 2.4

Physics Q&A
1

In question 2.4 of the tight-binding model questions, the exercise is to look for the effective mass. In the book (page 103) this is done for small k so a Taylor expansion can be applied on the dispersion relation to get [1-((ka)^2)/2] from the cosine. Looking at just the k^2 dependency you could derive an effective mass that is independent of k when equating this to (hbar^2)/2m. However here they ask for an effective mass that is dependent of k. How could I approach this slightly different question?

Thanks in advance!
Rogier

2

Try to calculate it using the definition of the effective mass

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