I'm afraid I'm quite rusty in my chemistry here. So, Fe 3+ would be 3d5. However, I'm not sure where the 3+ for La is coming from (unless it's just because its a common oxidation state). How can one assume that the most common oxidation state is the right one to choose?
So, La is 5d1, Fe is 3d6, As is 4p3, and O is 2p4. So Fe is close to half filling. But, so is As and O. So can we just say the bandstructure will compose of mostly Fe because of the half filling? Therefore, it is highly metallic and also the binding energy of the 3d6 should be much smaller?
Hi, I was hoping I could get some things cleared up. Recently my Solid State professor mentioned that we could simply, from the chemical formula, predict where the band crossings are going to be. For example, take LaFeAsO. Since La has a valency of +3, Fe of +3, As of -3, and O of -2, he...
Ah, thank you, I guess I need to work on keeping my indices separated. I appreciate all of the help (and patience!), JorisL. I think I have a better grasp of this now.
Ok, maybe. Let's see. So, let me know if this makes sense. Just working with the lowering operator:
\hat{a}_{l} |\phi \rangle= \hat{a}_{l}N\sum_{k}|\epsilon _{k}\rangle = \hat{a}_{l}N\sum_{k}\hat{a}^{\dagger}_{k}|0\rangle
From the anticommutation relations for fermions...
Ok, to be honest, the rigorous part of the proof is what is baffling me so much. A basis that spans our state will simply be the set of the \hat{a}^{\dagger}. But what next?
Well, I suppose due to orthogonality of the basis states, the\langle\Psi|\hat{a}_{k}^{\dagger}\hat{a}_{k}|\Psi\rangle would be \delta _{kl}\delta_{lk}? Since it seems the only nonzero states would be the point in which the creation operator creates a particle in the one that the annihilation...
Hi JoirsL, thank you for your response.
I will first answer the ground state question, in the question above you can see that he defines the ground state as {\Psi}, so it appears to me as if we are supposed to be working within this state.
The most general form of a state of a single...
Homework Statement
Homework Equations and attempt at solution
I think I got the ground state, which can be expressed as |\Psi \rangle = \prod_{k}^{N}\hat{a}_{k}^{\dagger} |0 \rangle .
Then for the density matrix I used:
\langle...
The intensity falling on it will be constant, yes. But the angle at which the light hits will determine how much is transmitted through the material. This is what I'm trying to figure out.
Hello,
I am currently working on a problem to calculate the light that makes it through a half circle. For example, say I put a cylinder out in the sun, where the intensity is known to be 1030 W/m^2. I would like to compute the intensity/energy/power that makes it into this. Now, given the...
Homework Statement
A gauge transformation is defined so as to leave the fields invariant. The gauge transformations are such that \vec{A}=\vec{A'}+\nabla\Lambda and \Phi=\Phi'-\frac{\partial\Lambda}{\partial t}. Consider the Coulomb Gauge \nabla\cdot\vec{A}=0. Find out what properties the...
Actually, this is a later part of the question (the d>>h). However, even if I try to simplify this in the integral, doesn't the integral look just as difficult?
Thanks guys. At least I know I'm getting the right process down. I'll have to talk to my professor to see if he expects this integral to be solved (through computation means or something).
Thanks for catching that. I actually have that down on my paper, I guess I forgot to put it down in the...
Homework Statement
A charge Q is uniformly distributed with linear density λ over a helix parameterized as \vec{r}=acos(\theta)\hat{x}+asin(\theta)\hat{y}+ \frac{ h\theta}{2 \pi}\hat{z}, where a and h are positive constants, and 0<∏<2∏.
a) Find the charge Q
b) Find the electric field on...
This is from section 2.3 in Griffith's book on the harmonic oscillator, and apparently this differential equation should be obvious (to move on in my reading, I need to understand this first). I'm not quite sure how to solve a second order ODE without constant coefficients, so help to get to the...
Maybe I'll have to present that to the professor. I thought that maybe she just wanted the same proof, but using Einstein notation for the matrices that make the transformation.
Ah, I see. I have been struggling with this problem for the past couple days and think I have developed a rough proof:
a and b are contravariant components of r' since they both give the magnitude of the vectors that add to r'. We found that:
\hat{e'}_{1}=\hat{e}_{1}...
Homework Statement
In the oblique coordinate system K' defined in class the position vector r′ can be written as:
r'=a\hat{e'}_{1}+b\hat{e'}_{2}
Are a and b the covariant (perpendicular) or contravariant (parallel) components of r′? Why? Give an explanation based on vectors’ properties...
Thanks guys, you've been a great help. I think I was able to reach a (somewhat) basic understanding of the notation. I have figured out that the indices almost "cancel out", from what Muphrid was saying about the requirement of both an index up if it shows up down, and vice versa. Also, in...
I'm having a difficult time describing what I'm having trouble with because I'm very lost in the notation. http://sces.phys.utk.edu/%7Emoreo/mm12/hw2/hw21n.pdf. I've figured out the actual transformations, but I am lacking the ability to express these in the correct notation. For example, take...
Ok, so here's my problem. I just graduated with a mathematics degree and am going full force into a physics graduate program. I'm taking a course called mathematical methods for physicists, in which the first subject is tensors. Everyone else seems to be comfortable with the material, but me...