Does anyone have any experience using Gregory Snider's 1D Schrodinger/Poisson solver? I'm trying to do some simulations of a quantum well my group is studying, and I'm not sure if I'm doing something wrong or if the code is buggy or if I'm just interpreting the results incorrectly. Here's the...
Say you have a Yukawa potential (a.k.a. screened coulomb potential) V(r) = -\frac{e^2}{r}e^{-rq} where q is the inverse screening length, how would you find the critical q for having bound states? I'm working on reproducing N.F. Mott's argument about the critical spacing of a lattice of...
It's from problem 12.2 - essentially it's valid near a maximum or minimum in the band (so you get an approximately quadratic dispersion). I haven't solved the problem yet, but I think the comment on page 568/569 about an ellipsoidal constant energy surface is key (in addition to the...