Understanding Electron Kinetic Energy in Quantum Wells

[rts20]

Hello to All !
I have a question that Whenever an electron from bulk material trapped by a quantum well that electron's 3rd dimensional kinetic energy component vanishes, But where that goes, is it added to the other 2 dimensional kinetic energy components..?

 

[rts20]

What i am asking is electrons in bulk semiconductor have 3 degree of freedom so they have 3 dimensional kinetic energy component, but Whenever an electron from bulk material captured by a quantum well (where it has only 2 degree of freedom) that electron's 3rd dimensional kinetic energy component vanishes., But where that goes, is it added to the other 2 dimensions?

 

[rts20]

When electrons in bulk material they have 3 degree of freedom(moves freely in all 3 directions) and hence their kinetic energy is 3 dimensional. but whenever electrons confined to quantum dot it's all 3 degree of freedom vanishes and so is their kinetic energy also losses..?

 

[mfb]

(I merged your threads)

You can (but don't have to) still have discrete excitations. It is a bit similar to the electron levels in an atom.

 

[MarcoJV]

Why should an electron in a semiconductor have the same energy (or possibly have) as a quantum dot? Naturally the description of the quantum dot has a degree of freedom less.

 

[ZapperZ]

This whole thread is very strange, mainly because of the question on the "kinetic energy". Do you also ask for the kinetic energy in a 1D quantum well problem? After all, it is practically the same thing. It is also unclear what exactly is the question of interest here. Is it a question on reduced dimensions in solids, or a question specifically on the band diagram of a quantum dot?

As it is now, the question itself is going in all different dimensions. I wish it could have been reduced to zero dimension.

Zz.

 

[rts20]

I am also so confused..What are these discrete energy levels in quantum dot and what type of energy(potential or kinetic energy) electrons will have if they lies in these discrete level..??

 

[ZapperZ]

I am also so confused..What are these discrete energy levels in quantum dot and what type of energy(potential or kinetic energy) electrons will have if they lies in these discrete level..??

Are you saying that you are confused with your own questions? Now that's precious!

You have not addressed the question for clarification that I asked. So this response doesn't add anything to clear up the confusion.

Zz.

 

[rts20]

Are you saying that you are confused with your own questions? Now that's precious!

You have not addressed the question for clarification that I asked. So this response doesn't add anything to clear up the confusion.

Zz.

What i am asking is that in some books these discrete levels are treated as electrons kinetic energy while in some books they are electrons potential energy levels,which one is correct..? that is my confusion.

 

[ZapperZ]

What i am asking is that in some books these discrete levels are treated as electrons kinetic energy while in some books they are electrons potential energy levels,which one is correct..? that is my confusion.

Please cite these sources and the exact phrasing.

But besides that, I asked you why you think this is any different than a simple 1D potential well problem that we all have done in intro QM. You never answered that.

Zz.

 

[rts20]

Please cite these sources and the exact phrasing.

I googled a lot to find these topics from my old books but i didn't find exact.
But i just managed few..
here in this slide from this http://faculty.uml.edu/cbaird/QCLPresentationApril2011.pdf shows that the bottom of discrete energy level in quantum well is Potential(P.E),
while in this slide from this site shows that the energy of discrete level equal to kinetic(K.E),
because all the energy of electron in quantum well is kinetic(E_n) from this pdf first page too.

But besides that, I asked you why you think this is any different than a simple 1D potential well problem that we all have done in intro QM. You never answered that.
Zz.

QM intro..? I think i missed that, But in every quantum well topic they says that electrons potential energy in QW is zero and all the energy is kinetic only..
but i think these discrete energy levels(quantization E_n) must be potential and kinetic energy is only due to electron motion in non-confinement direction(K_xy) as shown here.

 

[mfb]

The photobucket links don't work for me. Which page of the second set of slides do you mean?

that the bottom of discrete energy level in quantum well is Potential(P.E),

At k=0, the kinetic energy is zero. Not that it would matter, as only energy differences are relevant.

There is no energy eigenstate at exactly k=0. While there are states with very low kinetic energy in bands in solids, this is no longer true for quantum wells with a very limited spatial size.

But in every quantum well topic they says that electrons potential energy in QW is zero and all the energy is kinetic only..

The definitionof absolute potential energy is arbitrary. It is convenient to set it to zero inside a quantum well, but this is completely arbitrary.

 

[rts20]

The photobucket links don't work for me. Which page of the second set of slides do you mean?

the second set of slides also just like this pdf first page, where the eigenstate energy (E_n) is treated as kinetic energy of electrons in QW.

There is no energy eigenstate at exactly k=0.

I can understand that the lowest eigenstate (E₁) starts from K₁ as shown here .

what i can't understand is that eigenstate energy (E_n) is electrons kinetic energy or potential energy ? I think according to E-K digram E_n must be kinetic energy of the electron with momentum K_n, is that right..?

 

[ZapperZ]

the second set of slides also just like this pdf first page, where the eigenstate energy (E_n) is treated as kinetic energy of electrons in QW.

I can understand that the lowest eigenstate (E₁) starts from K₁ as shown here .

what i can't understand is that eigenstate energy (E_n) is electrons kinetic energy or potential energy ? I think according to E-K digram E_n must be kinetic energy of the electron with momentum K_n, is that right..?

The problem here is that you're trying to relate "k" with kinetic energy, and in this scenario, it doesn't work.

Let's back up a bit and go over something that you should already know (and which I now have doubts since you appear to have missed the 1D quantum well in intro QM). When you do tunneling phenomena, you define kinetic energy as E_k = E - V. You do not define it in terms of "k", the wave number. So already for a "traveling wave" case, you simply can't directly use k.

But now, you not only can't directly relate k to kinetic energy, you also have a standing wave situation. These are not traveling wave solution to the Schrödinger equation. All the wave function can tell you is the probability of where the particle is inside the well, and the energy state.

This is no different than asking for how fast an electron in an s-orbital of an atom is moving or orbiting around the nucleus.

Zz.

 

[rts20]

The problem here is that you're trying to relate "k" with kinetic energy

yes because as i already told i have confused with electrons energy and momentum in quantum well..
here in this first https://www.researchgate.net/profile/Thomas_Nann/publication/229622377/figure/fig6/AS:273339474247686@1442180617554/Figure-8-8-Free-charge-carriers-in-a-solid-have-a-parabolic-dispersion-relation.png eigenstates are fixed inside e-k diagram with fixed energy and momentum always non-zero,
in this second pic2 e-k diagrams are starting from fixed eigenstates where the only momentum starting from zero,
which one of them is correct and what is the meaning of them ?