I have to plot the conductivity dependence of temperature and I have problems with obtaining the right dependency of \mu and n. But let's focus only on carrier concentration first.
For n I used the third equation. From what I understand N_D is a constant. I want my plot to look like this:
But...
\omega= \frac{2\pi c}{\lambda}=\frac{2 \cdot \pi \cdot3\cdot 10^8}{500 \cdot 10^{-9}}\approx 3.77\cdot 10^{15} Hz
Which is still less than \omega_p so R=1.
The Drude model was the only one we've discussed during the lecture, so I would expect it is used in the solution. Thank you for clarifying this! I'll need to ask my tutor whether we should use something different that wasn't covered yet.
Note: for some reason frequency on this lecture is indicated by \omega.
I wanted to calculate the reflectance using one of these equations that were given to us during the lecture:
R=1 where \omega < \omega_p...
It's a problem formulated by my professor.
After you post I contacted him and indeed, he made a mistake in the homework statement, as the last operator \hat{c}_{-k \downarrow} should be conjugated for the expected value to be one. In the original statement, the value will be 0.
Thank you!
We have a one dimensional lattice with a lattice constant equal to a (I'm omitting vector notation because we are in 1D). The reciprocal lattice vector is k_n=n\frac{2 \pi}{a}.
So to get the nearest neighbour approximation I need to sum over k = -\frac{2 \pi}{a}, 0, \frac{2 \pi}{a}.
If I...
Ok, I plugged in the numbers and I might still need a little help.
Using the result from the answers in c), I came to a conclusion that the reduced mass (I'm going to denote it by \mu must be equal to \mu = 9.2 \cdot 10^{-25} \ kg because F= kx = k\cdot 1 = \mu \omega_0^2 so we get 23 = 25...
The last one got me confused because the lecturer just waved their hands saying "well you know it's the atoms". But that explains a lot.
Thank you! Really, I needed some guidance 😅 Have a nice day!
I got these values from the attached figure: n_{st}=2.4 and n_{\infty}=1.3.
Ok, now the explaining.
I define a complex dielectric function (permittivity) as
\widetilde{\varepsilon} = \varepsilon_1 + i \varepsilon_2
So \varepsilon_1 is the real part of the dielectric function and \varepsilon_2...
a) I managed to obtain some results that are roughly around what is given in the answers.
Because \varepsilon_{st} and \varepsilon_{\infty} are values of \varepsilon_{1}, I used this approximation:
n\approx \frac{1}{\sqrt{2}} (\varepsilon_{1}+\sqrt{\varepsilon_{1}^2})^{1/2}
-> \varepsilon_{1} =...
The limit itself is pretty easy to calculate
##lim_{T->0} \ lim_{\mu->\epsilon_F} \ (e^{\frac{(\epsilon_F - \mu)}{kT}}+1)^{-1} = \frac{1}{2}##
But I'm very confused about changing ##\epsilon_\vec{k}## to ##\epsilon_F##. Why do we do this?
I have a problem with finding the energy of an electron in an FCC lattice using the weak potential method. We did that for a one-dimensional lattice during class, and I know that there was a double degeneration at the boundaries of the first Brillouin Zone. However, I'm not sure what...