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Talk:Free electron model

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is this article equivalent or related to [[1]] ? - Schroedi 16:00, 26 February 2007 (UTC)[reply]

As the free electron model is surprisingly successful in explaining many experimental phenomena, are there any model shortcomings that explain phenomena in a wrong way? --Abdull 09:04, 6 November 2007 (UTC)[reply]

it does not explain the energy band gap in an electron-ion perodic lattice PersonaErazed (talk) 19:03, 7 March 2016 (UTC)[reply]

This free electron model often known as the Sommerfeld theory of metals. Rod57 (talk) 00:09, 20 June 2008 (UTC)[reply]

This article starts with "In solid-state physics, the free electron model .." implying that the term is only used in solid-state physics. This ignores the method with the same name introduced by J. R. PLatt in the late 1940s and 1950s where the pi system of conjugated hydrocarbons are treated just like the "particle in a box" method. It was also applied to conjugated cyclic systems such as benzene. How best can this be introduced into the article? --Bduke (Discussion) 06:37, 26 April 2010 (UTC)[reply]

"Traveling plane waves restlessly heading for their Final Destination"

Eh? — Preceding unsigned comment added by 94.12.16.145 (talk) 10:41, 6 June 2011 (UTC)[reply]

The most recent issue of the CERN Courier makes an oblique reference to a free electron exhibiting a gravitational acceleration constant of 0, instead of 9.8 m/s^2. Has this phenomena ever been studied in any more detail? Is there a better reference? It might be worth adding to the page if it can be substantiated. Here's the text: "Measurements based on dropping electrons led to a value of the acceleration of gravity, g, consistent with zero" — Preceding unsigned comment added by 96.25.137.97 (talk) 16:46, 2 March 2014 (UTC)[reply]

If you carefully read the article, they used this example as proof that stray fields can mess up results. Chris2crawford (talk) 03:04, 3 May 2014 (UTC)[reply]

The following definition of E(\omega) is misleading, because it implies E_0 is a constant w/r omega.

 ${\displaystyle E(\omega )=E_{0}e^{-i\omega t},\quad P(\omega )=P_{0}e^{-i\omega t}}$

It would make more sense to say E(t), with E_0 as the constant amplitude. It is this amplitude, which is actually a function of omega. Correction:

${\displaystyle E(\omega )=E_{0}(\omega )e^{-i\omega t},\quad P($t)=P_{0}(\omega )e^{-i\omega t}}
  

Then after taking the derivatives, you factor out ${\displaystyle e^{-i\omega t}}$, drop the 0, and the rest is the same.

Chris2crawford (talk) 03:15, 3 May 2014 (UTC)[reply]

The section entitled Solution of the Schrödinger equation derives plane wave solutions for the Schroedinger equation. It is wordy and long, and contains some mathematical solecisms. But more important -- it belongs in a different article! It is too elementary and to detailed for this article. That is why we have links. It should be greatly reduced or removed. 178.39.122.125 (talk) 13:56, 1 January 2017 (UTC)[reply]

The derivation in the section Dielectric function of the electron gas is incoherent.

(1) It has a restoring electric fieldof

${\displaystyle E={\frac {nex}{\epsilon _{0}}}}$

and later a polarization density

${\displaystyle P=-nex}$.

But it also has a dielectric constant

${\displaystyle \epsilon =1+{\frac {P}{\epsilon _{0}E}}.}$

Unfortunately, when you plug in the above values of E and P into this equation you get

${\displaystyle \epsilon (\omega )=1+{\frac {-nex}{\epsilon _{0}(nex/\epsilon _{0})}}=1-1=0.}$

This makes no sense.

(2) Another problem I have with this derivation is that it says that we get a harmonic oscillator equation, but the equation is not exhibited. I want to see the equation!

178.39.122.125 (talk) 14:16, 1 January 2017 (UTC)[reply]

This article was the subject of a Wiki Education Foundation-supported course assignment, between 7 January 2022 and 18 March 2022. Further details are available on the course page. Student editor(s): Wongzh (article contribs).