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Jul 9, 2019 at 12:31 comment added garyp @thermomagneticcondensedboson Perhaps I said too much in too few words. I first address the OP's concern about the fact that the dispersion relation is not parabolic. Then I say "different values of 𝑘 label exactly the same wave vector", trying to explain why the same wave vector can have multiple values for energy. Same wave vector, but different $k$. Finally, instead of reposting an earlier post made that has a lot more detail, I pointed to it.
Jul 9, 2019 at 12:06 comment added untreated_paramediensis_karnik It looks like you have totally misunderstood the question, at least that's the impression I get. It doesn't matter an iota whether you consider the free electron model or the nearly free electron model, in that in both cases one still gets the same feature described by the asker, namely that E(k) yields several values for a single value of k.
Apr 13, 2017 at 12:39 history edited CommunityBot
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Oct 19, 2015 at 17:34 history answered garyp CC BY-SA 3.0