I understand this is an undergraduate course, I have tried to access graduate quantum physics courses on this site but it seems none is available. Is there a course in quantum electrodynamics or quantum optics?
I don't understand how is d^3 k = k^2 * dΩ * dk. I guess the idea is that the dimensions of the infinitesiminal cube are k, k* dΩ and dk. I get why are there k* dΩ and dk, but what is k in this context? Height? Width? length?
too late but in case anyone needs it in here... What he has drawn is in k-space, 3D k-space. Now what we need is a volume element in this K-space. For 3D, u need 3 basis vectors. Change in two will get u the area and the other wd be like height or dimension in which u can span the area to get to the volume. Here he has used solid angle instead of angle, which is like a 2D counter-part of angle. Remember how we have small change in angle, dtheta, times radius, r, gives us the arc length. Similarly, if u consider a small change in solid angle domega ...(2D counterpart of dtheta)..., times the r^2 ...(2D counterpart of r)... it gives us the area ...(2D counter part of length)... that the small cone spans at the surface end. This is the area which we have to multiply with the change in radial direction dr to get to infinitesimal volume element. Here, instead of r use k.... .'. k^2 * domega * dk
I am studing DFT and I have come up with many kind of tutorials and lectures about Density of States but this one is simple and expanatory. Amazing!!!
@Mae Barker wtf guys ?
Thank you sir
Indeed anazing explanstions and teacher
very good explanation of about what density of states are?
I understand this is an undergraduate course, I have tried to access graduate quantum physics courses on this site but it seems none is available. Is there a course in quantum electrodynamics or quantum optics?
I don't understand how is d^3 k = k^2 * dΩ * dk. I guess the idea is that the dimensions of the infinitesiminal cube are k, k* dΩ and dk. I get why are there k* dΩ and dk, but what is k in this context? Height? Width? length?
too late but in case anyone needs it in here...
What he has drawn is in k-space, 3D k-space.
Now what we need is a volume element in this K-space.
For 3D, u need 3 basis vectors. Change in two will get u the area and the other wd be like height or dimension in which u can span the area to get to the volume.
Here he has used solid angle instead of angle, which is like a 2D counter-part of angle.
Remember how we have small change in angle, dtheta, times radius, r, gives us the arc length. Similarly, if u consider a small change in solid angle domega ...(2D counterpart of dtheta)..., times the r^2 ...(2D counterpart of r)... it gives us the area ...(2D counter part of length)... that the small cone spans at the surface end. This is the area which we have to multiply with the change in radial direction dr to get to infinitesimal volume element.
Here, instead of r use k.... .'. k^2 * domega * dk