Here are some notes on how to find the (approximate) energy and nature of electron states in crystalline solids. (Starting in 1-dimension, of course.) There will be a part 2, where we actually calculate that thing at the end (Eq) (approximately). If you want to do that on your own in the meantime, I think you can. To get things started, I would suggest that the thing in the denominator is pretty much 1, and so you can focus on the numerator and just look for the 4 or 5 largest terms from the infinite serieses. For a concrete case, attractive delta functions are perfect, (and you know what the solution is for just one of them).
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