In the beginning of the video you briefly went over how to calculate the energy density of a bulk material, introducing concepts like Boltsman approximation Fermi Dirac equation and more. However they were not explained in this playlist, can you refer to videos in which you elaborate on these concepts?
This has to do with how you want to solve the Schrodinger equation. You can solve it in terms of complex exponentials (in which case you can have negative kx and ky, this corresponds to traveling waves going -x and -y). *Or* you can solve it taking only the sinusoidal solutions, in which case kx can only be negative (or positive and negative kx mean the same thing). If you use the sinusoidal solution, you use 1/8 of k-space, if you use the exponential, then all of k-space. It's just a little harder to do with complex exponentials.
Maybe it's a silly question but why can K be a negative number? I am associating it with position vector x that can be with flipped sign. If what I am writing is correct then the energy density should be larger by a factor of 4, since 2*pi*k*dk will be a full square Thanks
If the quantum well is small, it’s usually better to treat the individual states separately rather than as a density. The approach in this video works well in practice as long as the dimension is large (>> 10nm or so)
Thank you so much for doing these videos!
In the beginning of the video you briefly went over how to calculate the energy density of a bulk material, introducing concepts like Boltsman approximation Fermi Dirac equation and more. However they were not explained in this playlist, can you refer to videos in which you elaborate on these concepts?
That was a great explanation!
Really nice and helpful video!!! I only have one question. Why is it a quarter of a circle in k-space? Can't we have negative kx and ky?
This has to do with how you want to solve the Schrodinger equation. You can solve it in terms of complex exponentials (in which case you can have negative kx and ky, this corresponds to traveling waves going -x and -y). *Or* you can solve it taking only the sinusoidal solutions, in which case kx can only be negative (or positive and negative kx mean the same thing). If you use the sinusoidal solution, you use 1/8 of k-space, if you use the exponential, then all of k-space. It's just a little harder to do with complex exponentials.
@@JordanEdmundsEECS Really great explanation! Thank you!!
Maybe it's a silly question but why can K be a negative number? I am associating it with position vector x that can be with flipped sign. If what I am writing is correct then the energy density should be larger by a factor of 4, since 2*pi*k*dk will be a full square
Thanks
Does this expression work for massless spin 1/2 fermions??
How is this different if it is a finite quantum well?
If the quantum well is small, it’s usually better to treat the individual states separately rather than as a density. The approach in this video works well in practice as long as the dimension is large (>> 10nm or so)
GOLD, but can you talk about parabolic potentials?
Mmm harmonic oscillators. Might have to make a few videos on those.