Talk:Lindhard theory

Citing Lindhart

"The article of Jens Lindhard is more often cited with the wrong page number (8) than with the correct page number (1). 501 wrong citations vs. 213 correct citations as counted in 2004. 8 is the number in volume 28 of Dan. Mat. Fys. Medd. The article starts with page 1."

As Toshiyouri pointed out in his edit April 8, 2016 and above, the reference J. Lindhard, K. Dan. Vidensk. Selsk. Mat. Fys. Medd. 28, 8 (1954) starts with page 1. However, this journal publishes single articles per issue, and does not continue page numbering across volumes. Referencing the paper using the issue number and excluding the page number is an appropriate method to cite the paper. I have edited the reference here so as to include both an issue number and a page number. Fbfree (talk) 19:40, 28 September 2016 (UTC)

References

High-Frequency Limit

I believe that under the 3d "Long Wave-length Limit" the result for the high frequency limit is derived. (see for example Advanced solid state physics by Philip Philips chapter 9.4). — Preceding unsigned comment added by 2001:6B0:1:1041:A117:9D:2B09:F8B7 (talk) 16:11, 13 January 2014 (UTC)

Article is inaccurate and confusing

This article is not written clearly,intuitively. The title implies a discussion of the physical background of TF screening. Instead, it offers a formal and not clearly justified discussion of the Lindhard formula (which can be actually discussed in another article devoted to this formula). A typical example of TF screening deals with the penetration of a static electric field in metals first studied by Rice (1928). This pioneered very interesting, productive and partially controversial discussion echoed in the modern analysis of nano-devices. None of this is reflected in the current paper.

TF screening is not necessary linear, but the paper only deals with linear effects. At the end of the paper, wires and cylinders are introduced practically out of of blue.

Some statements seem to me ambiguous.

Thomas–Fermi screening is one of many approximation methods for describing the screening (should probably say that TF approach is one of many theoretical approaches to electron screening) . Thomas–Fermi screening assumes that the total potential varies very slowly (TF theory actually defines the variation of the potential i.e. the screening length, without assuming that it is large [or the variation is slow]).

— Preceding unsigned comment added by Moshepar (talk • contribs) 23 July 2012‎

I moved the page since it does seem entirely about Lindhard theory, which is more general and complicated than Thomas-Fermi theory. I agree with all the complaints but I'm afraid I'm not sufficiently knowledgeable to fix them. --Steve (talk) 16:45, 30 November 2012 (UTC)

Problems with Displaying the Webpage

I use current versions of Firefox and MS Internet Explorer. Nonetheless, I obtain read error messages of the kind: Failed to parse(unknown function '\begin'): {\begin{alignedat}{2}\epsilon (0,\omega )&\simeq 1+V_{q}\sum _{{k,i}}{{\frac {q_{i}{\frac {\partial f_{k}}{\partial k_{i}}}}{\hbar \omega _{0}-{\frac {\hbar ^{2}{\vec {k}}\cdot {\vec {q}}}{m}}}}}\\&\simeq 1+{\frac {V_{q}}{\hbar \omega _{0}}}\sum _{{k,i}}{q_{i}{\frac {\partial f_{k}}{\partial k_{i}}}}(1+{\frac {\hbar {\vec {k}}\cdot {\vec {q}}}{m\omega _{0}}})\\&\simeq 1+{\frac {V_{q}}{\hbar \omega _{0}}}\sum _{{k,i}}{q_{i}{\frac {\partial f_{k}}{\partial k_{i}}}}{\frac {\hbar {\vec {k}}\cdot {\vec {q}}}{m\omega _{0}}}\\&=1-V_{q}{\frac {q^{2}}{m\omega _{0}^{2}}}\sum _{k}{f_{k}}\\&=1-V_{q}{\frac {q^{2}N}{m\omega _{0}^{2}}}\\&=1-{\frac {4\pi e^{2}}{\epsilon q^{2}L^{3}}}{\frac {q^{2}N}{m\omega _{0}^{2}}}\\&=1-{\frac {\omega _{{pl}}^{2}}{\omega _{0}^{2}}}\end{alignedat}} Ideas?

A few suggestions to improve the accessibility of this article and meet basic encyclopedic standards

Hi, I came to this article in search of some answers but struggled quite a bit. Partly, that's b/c in my view the article has a few basic issues:

• Not every reader is familiar enough with the subject, so it would be very helpful if all quantities of the initial formula were properly introduced. Currently, the quantity V is not explained at all; is it a potential (energy), or a volume, or something else? And where do the identities, that are later used, come from?
• What do q and omega stand for? I know they are a wave vector and a frequency, but of which wave?
• The same is true for E, although from knowledge of perturbation theory it could be deduced that it represents the energy.
• When I looked at the different cases, I realized that the electrons are treated as if they were free (~k^2) which is certainly an approximation that should clearly be stated - and potentially justified.

Is anyone familiar enough with the theory to be able to rectify those issues? Thanks! 132.181.230.132 (talk) 23:14, 6 November 2019 (UTC)