Dear course team,
I don’t understand how we should plot the dispersion band mentioned in question 3.2.
In the answer model it is said that we should look in the lecture notes. However, to the best of my knowledge we have never seen any dispersion relation as complicated as this one. It has almost always just been E= constant ± a square root depend on one k vector. I already tried plotting it with wolfram alpha however that of course gives a computational time error since we have no clue how the constants in the dispersion relation depend on each other.
Regards,
Stein Glastra
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I’m pretty sure it’s supposed to just be a parabola with avoided crossings (like the dispersion in the lecture notes). I’ve plotted it here Graphing Calculator. The constant involving the mass and planck constant is many order of magnitudes smaller than the lambda/a (which should be roughly of order 1 since the light was supposed to be of the same order of magnitude as the lattice spacing).
As a result, the lambda^2/a^2 will dominate the k-term inside the square root and the entire thing depends mostly on just the k^2 term, meaning it’s just a parabola.
This is indeed the correct answer: all nearly free electron model dispersions look the same.