Density of States | Free Electrons

References:
[1] Ashcroft, Mermin, "Solid State Physics".

Table of Contents:
00:00 Introduction
00:39 Free Electron Model
00:56 Energy Levels
01:47 How Many States per Energy?
02:53 Sum to Integral
03:31 1D
03:49 2D
04:11 Van Hove Singularity

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TheFatRat - Fly Away feat. Anjulie

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[AnubhavMadansure]

Very neat and nice explanation. Thanks a lot. Just a correction at 3:25, for the 2-D density of states the denominator has square of h-bar (or h-cross or h-cut).

[flavioryu]

Fly away from TheFatRat at the end just makes the video even better!

[ngdnhtien]

If we consider free electrons, then the solutions to the Schrödinger equation are plane waves, no? How come we're having standing wave solutions (at 1:05), which assume electrons are trapped inside a cubical potential?

[SampleroftheMultiverse]

Thanks for your interesting video.

Area under a curve is often equivalent to energy. Buckling of an otherwise flat field shows a very rapid growth of this area to a point. If my model applies, it may show how the universe’s energy naturally developed from the inherent behavior of fields.

Your subscribers might want to see this 1:29 minutes video showing under the right conditions, the quantization of a field is easily produced.

The ground state energy is induced via Euler’s contain column analysis. Containing the column must come in to play before over buckling, or the effect will not work. The sheet of elastic material “system”response in a quantized manor when force is applied in the perpendicular direction.
Bonding at the points of highest probabilities and maximum duration( ie peeks and troughs) of the fields “sheet” produced a stable structure when the undulations are bonded to a flat sheet that is placed above and below the core material.

Some say this model is no different than plucking guitar strings. You can not make structures with vibrating guitar strings or harmonic oscillators.


At this time in my research, I have been trying to describe the “U” shape formed that is produced before phase change.

In the model, “U” shape waves are produced as the loading increases and just before the wave-like function shifts to the next higher energy level.

Over-lapping all frequencies together using Fournier Transforms, can produce a “U” shape or square wave form.

Wondering if Feynman Path Integrals for all possible wave functions could be applicable here too?

If this model has merit, seeing the sawtooth load verse deflection graph produced could give some real insight in what happened during the quantum jumps between energy levels.

The mechanical description and white paper that goes with the video can be found on my LinkedIn and YouTube pages.

You can reproduce my results using a sheet of Mylar* ( the clear plastic found in some school essay folders.

Seeing it first hand is worth the effort!

[wikiaslam]

Nice explanation really love to see your video love u

[Dark-tkxu]

I was under the impression that the electrons in the free electron model (i.e., Sommerfield model) are travelling waves.

[cjbercasio]

Thanks for the neat explanation. Can I know what page on Ashcroft’s Solid State physics this is? I want to read more and know more stuff about it 😁

[AnaIsabelMendesTeixeira]

This video and the playlist helped a lot, but maybe you could put the playlist in a more logical order?

[consciousness]

oh... your english is so anstrengend... Its not bad, just sounds like you have to put alot of effort in which makes it strenuous to listen to