Density of States in a 3D semiconductor

[@rozputinpvp]

At the end after you plug everything in and change m into m*: Around 11:30 Where does the 8 come from? Is it b/c it was calculated for 1/8th of the sphere n now you're plugging in that x8 or what? Or is it b/c you've changed m= 8m* ? Also around 5:12 you're saying that the radius of the sphere is k_x times k_y times k_z, but shouldn't radius be defined as: r = (k_x^2+k_y^2+k_z^2)^(1/2)? And then that expression would be cubed b/c it's the sphere volume. K_x times K_y times K_z would give you volume of a rectangle.

[@Alexbingov]

Hey Vitaly, That 8 comes from Unit Cell consideration.like If you see a simple cubic unit cell corners it contains 8 lattice points.

[@tanmaykumarmanna198]

Vitaly Fedotov

[@IDoNotFeelCreative]

"I can die happily ever after" that's how I feel when confronting any math problem... Just let me solve this and i can die contented afterwards:)

[@SpirallingUpwards]

Where did you derive your E - k relationship?

[@chrisevers589]

I know that this is a very simple question, but what is the meaning of the wave function here? What does it physically represent?

[@AtulKumar-ke8gq]

There is no physical meaning of wave function as it is a complex function. It only makes sense when multiplied with its own conjugate....which will give probability

[@madhavsirohi2225]

I really Needed this!!!

[@Teeziel]

this is an excellent explanation.

[@MrJuma95]

where does the 8 come from in the end?

[@ahmedtahraoui6619]

+Guru Bharan (h bar = h/2 pi)

[@ahmedtahraoui6619]

+Michael Ngodori (hbar=h/2pi)

[@kajalumrethwala9330]

4:52 how it is 1/8 of sphere

[@ahmedamer5870]

Boundary conditions state that k_x, k_y and k_z should have only positive( non-zero) values, which is only satisfied in the first octant of the sphere

[@serasen8316]

@@ahmedamer5870 thank u

[@franklinelel]

indeed N is the number of free electrons in the sample and N/2 will be the number of states since each state holds two electrons. one spinning up and one spinning down.

[@MiladP]

Very good, keep it up.

[@somoshreechatterjee3105]

Can you please tell me how the volume in K-space becomes V=(pi/Lx)*(pi/Ly)*(pi/Lz)? Where from the "pi" comes?? please help. i couldn't figure it out. Help

[@erikeisenach9949]

+Somoshree Chatterjee The spacing between each k-value is pi/L since the boundary conditions restrict each k value to be an integer multiple of pi/L. So the first is 0, the pi/L then 2*pi/L, etc.. Hence the distance between one k-value and the next is pi/L correct? Then since the volume of a box (in this case a cube) is each side length multiplied by one another (x*y*z) you have the side length in kx (which is pi/Lx) times the side length in y (which is pi/Ly) times the side length in z (which is pi/Lz). In short (pi/Lx)*(pi/Ly)*(pi/Lz)

[@Τουκ]

cant stop thinking of Rajesh Koothrappali but still great explanation thanks :P

[@dikshagupta3371]

Thnkssssss

[@shubhangisingh4663]

Plz hindi m bhi yhe video bna do.......,.....