Posted by Steve Simon on February 26, 2013, 1:01 pm, in reply to "Heterostructure well"
Hi again, I realize I did not answer your first question. Does crystal structure on small scales (even if there are no defects) change the story. The short answer is "not much". If you want to convince yourself of this, you might try the following calculation (maybe I should have put this calculation as an exercise in the book  I think it is probably quite hard, but might be fun to think about even if you don't solve it). Consider a tight binding chain in one dimension with hopping t (and spacing between sites is 1). suppose that the onsite energy of site n is given by E_n = V, for n Now consider the band structures of the two regions (as if the regions were infinite). They both have the same effective mass m^* = hbar^2/(2 t). And the two regions have different potentials by V. Now treating this as just a free particle with effective mass m*, solve the continuum schroedinger equation for the eigenstates and see how much these differ from the above more exact picture. I haven't actually done this calculation, but i might try it when I get a chance! 
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