Talk:Nearly free electron model

message: Re this edit - it is definitely true that a function sines and cosines can be expressed as an expansion in plane wave form, I am not sure that it is useful here. The whole point of the nearly-free model is to work from the easy case of free electrons, then apply periodicity. The wavefunction could also be expressed as a linear combination of any other appropriate set of basis functions, it is just that generally doing so will not provide physical insight. Am I missing something here? - 2/0 (cont.) 08:40, 15 November 2010 (UTC)
thread_title:  Oscillating functions expressed as plane waves 

message: The section "Introduction - a heuristic argument" contributes little or nothing. It reminds me of what I scribble to myself when I'm just starting on a problem -- I take a few integrals just to get the measure of the problem, at random, but it doesn't mean much ! 
It should be deleted or replaced by something from a book.
The section has two parts:
(a) A correct derivation of the average energy of a plane wave of wave number k. This works for all k, not just k small as was originally assumed.
As the narrator himself points out, we have not done anything significant at this point.
(b) An attempt to say something about the interaction of the peaks of the plane wave (I guess?) with the periodic variation of V as k gets near the size of the unit cell of the lattice. It is hard to tell what is going on because the narrator appears to have switched from exp(ikx) to sines and cosines without telling us what he is doing. As a result, this part is not coherent.
The narrator tells us several times that it is important that k is in the "Brillouin call" but never really capitalizes on this.
Of course, it is true that "something happens" when k starts to rhyme with the periodicity, but we have yet to hear (clearly) what.
A particularly egregious mistake is dividing by k, which is a vector. The result is the vector equation r=±π/2k. 
I would recommend deleting this section. Or replacing it by something from a book.  — Preceding unsigned comment added by 178.38.12.166 (talk) 17:14, 9 November 2014 (UTC)
thread_title:  Nonsense 

message: I was shocked to see that this much nonsense in "Introduction – a heuristic argument" survived for so many years. This introduction adds nothing, has no conclusion, and is utterly wrong. I am deleting it. First part was introduction to Euler's formula for exp(ikr). It says: "The expression of the plane wave as a complex exponential function can also be written as the sum of two periodic functions which are mutually shifted a quarter of a period." Should we forget the little i in front of the other function? Next, the expression for <T+V> is given, and it's said it shows that the energy is lowered. Maybe it does, but not here: " This isn't a very sensational result and it doesn't say anything" ... " about what happens when we get close to the Brillouin zone boundary." (No idea why the boundary is important). Next, cos(kr) and isin(kr) parts are discussed for different k's (but let's forget that we're allowed to add any phase to these). |psi|^2 (which equals "1" everywhere) is decomposed into (1-cos(2kr))/2 and (1+cos(2kr))/2. It could have been decomposed into 1/2-(2kr)^42 and 1/2+(2kr)^42 just as well, but that wouldn't prove the "point": "As a result the aggregate will be split in high and low energy components when the kinetic energy increases and the wave vector approaches the length of the reciprocal lattice vectors. The potentials of the atomic cores can be decomposed into Fourier components to meet the requirements of a description in terms of reciprocal space parameters." Still trying to figure out what this means. Time to delete, or else I will lose my faith in wikipedia ("one can be wrong, but many can't").  — Preceding unsigned comment added by Ponor (talk • contribs) 12:30, 28 May 2020 (UTC)
thread_title:  Nonsense II