Talk:Particle in a one-dimensional lattice

Oh no, all the images are untagged! Could somebody draw new ones? The guy who put them here hasn't been around wikipedia for a year. Pfalstad 17:12, 7 October 2005 (UTC)

Does someone have a standard textbook on QM to check if the 4 by 4 matrix is correct? I suspect that there is a sign error in the fourth row, fourth column.

I am not able to check the 4 by 4 matrix, but I suppose that the same sign error is in the last equation. The Kronig-Penney relation is $\cos(ka) = \cos(\alpha a) + P\frac{\sin{\alpha a}}{\alpha a}$. (Albeverio at al.;Solvable models in quantum mechanics)

I just derived the 4 by 4 matrix and found it to be correct, at least for k = 0 (the case I need for my work). I also calculated the full determinant, and it matches as well. --98.250.181.247 (talk) 19:38, 12 May 2012 (UTC)

Error in Image
There's a picture of one period -b < x < a-b that labels the end of the interval as 'a'. This is wrong and confusing. Someone should upload a new image. —Preceding unsigned comment added by 129.105.207.198 (talk) 05:38, 2 December 2007 (UTC)

That image may now be gone, but the current image labeled the interval 0<x<a+b as a. a+b should be one period of the square wave, not just a. — Preceding unsigned comment added by 129.21.213.175 (talk) 21:45, 9 December 2013 (UTC)

Proposed merger
This article is much more substantive than One-dimensional_periodic_case so perhaps that article should just be deleted. I didn't want to do anything rash though, so I decided to start a discussion. By the way, has there never been an image called Potential-approx.PNG? I could probably create one. Alison Chaiken 05:29, 8 January 2006 (UTC)


 * Yes, we should merge. The three images in this article were all untagged, so they got deleted.  Pfalstad 11:00, 8 January 2006 (UTC)

Proposed Linking
This page should be linked/added to the "band gap" article. As this concept is so fundamental to band gap theory, it should be obvious. This exact treatment is used in my solid state physics textbook on the chapter that derives and explains bandgaps (same chapter as bloch's theorem, the central equation, etc)

you will notice, in the band gap article, that no mention is made to the physical/mathematical source of the bandgap (eg the way it crops up in computing the eigenvalues of a periodic hamiltonian with potential expressed in fourier space). —Preceding unsigned comment added by 128.111.148.212 (talk) 21:23, 2 February 2010 (UTC)

3D to 1D reduction?
I removed the following statement:

The problem can be simplified from the 3D infinite potential barrier (particle in a box) to a one-dimensional case.

Sounds like this was copied from a particle-in-a-box article (where one indeed can separate variables for a rectangular box), but I don't think a 3d periodic potential could be reduced to 1d (at least I don't see how).

64.149.234.79 (talk) 05:22, 19 October 2010 (UTC)

Editing
Dear All, this article needs some serious editing. The entire section on the Kronig-Penney model is at best confusing and useless and at worst incorrect. — Preceding unsigned comment added by 70.162.92.242 (talk) 06:15, 3 May 2012 (UTC)