Ah! My reference text misled me. It seems to be the case that Δn = 0 must hold even for the finite square well.
Consider two bound states |1> and |2>, with distinct energies E1 and E2, and consider the matrix element,
\langle 1 | H | 2\rangle.
H can operate to either the left or the right...
I've been reading up a bit on semiconductor quantum wells, and came across a selection rule for an infinite quantum well that says that "Δn = n' - n = 0", where n' is the quantum well index of an excited electron state in the conduction band, and n is the index of the valence band state where...
Is there an easy-to-articulate difference between a polaron and an electron exhibiting electron-phonon coupling? Until yesterday, I had been under the impression that the difference between the two phenomena was related to the strength of the coupling. However, I looked up "polaron" on...
I've mostly been looking at Ascroft & Mermin, pp. 225-229, but also Ziman (Principles of the Theory of Solids), pp. 184-186. There's a bit too much material to quote, but after closer inspection, I guess Ashcroft and Mermin make no statements about the sign of the energy of holes, though their...
I've been playing around with some ideas of electron-hole pairs in semiconductors lately, have realized that I'm confused about some basic conventions that maybe the physics forum community could help clear up.
Let's imagine that we have a direct gap semiconductor initially at zero temperature...
Hi all,
I'm working on a Green function chapter of my dissertation, am referencing the equation,
G(k,\omega) = \int_{-\infty}^\infty \frac{A(k,\omega')d\omega'}{\omega - \omega' + i0^+},
and I am trying to figure out the best way to credit it. I have noticed that condensed matter texts...
Not exactly. The volume of the BZ divided by the volume of a k-state is equal to the total number of available k-states for a given band in the system, i.e., the number of slots in the band that are available for charge carriers (electrons) to inhabit. Thus, if the volume enclosed by the Fermi...
Great! I am declaring my original post to be entirely correct. Thanks for everyone’s comments.
This statement that the diagram is incomplete is not right, as far as I can tell. It would only be accurate for the example with electrons and photons in a vacuum, and the reason is that the diagram...
Thanks, and yes, the typical electron-phonon interaction is exactly what I am trying to describe. I am interested to know if Feynman diagrams would be an appropriate way to describe the electron-phonon interaction in a "cartoon" fashion. If so, what do the lowest-order diagrams look like?
Can you elaborate on what you mean when you say that the Feynman diagram is incomplete?
Nomenclature aside, what I am trying to ask is, in a metal or semiconductor, can one electron in a state at energy \omega spontaneously scatter into one electron at a lower energy state \omega-\Omega, plus...
In a metal, can one electron decay into one lower-energy electron plus one phonon? (i.e., can the attached Feynman diagram occur?)
If we replace phonons by photons and consider the process in a vacuum, I guess this is prohibited because you can always boost to a frame where the incoming and...
Thanks. Funny you should mention writing your thesis...I'm getting ready to do that myself in a month or two, which is why I am interested in getting a better handle on these concepts ;)
I know--because of Noether's theorem--that continuous rotational symmetry implies conservation of angular momentum, and that continuous translational symmetry implies conservation of linear momentum. It also turns out that the discrete translational symmetry exhibited by a Bravais lattice...
Can you refer me to any sources where this symmetry analysis is discussed at a "textbook" level? Surely somewhere out there, there must exist a source that can explain why the d-wave form of the gap Δk should be given by
\Delta_k = \Delta_0 \left( \cos k_x - \cos k_y \right)
as opposed to...
The answers to your questions are rather complicated, so I imagine it will be a little bit hard for anyone to answer adequately in a single paragraph or two ;)
Do you have access to any of the standard physics textbooks? I seem to remember that Chapter 5 of "Introduction to Quantum Mechanics"...
The integral I am trying to solve is a version of a Fourier transform, so it would be better if the approximation were r-dependent.
I was thinking that integrating by parts twice would sharpen the 1/√(...) piece and make it look like a delta-function. Then the integration would be easy if I...
I'm looking for a way to write down an analytic approximation for the following integral:
\int_0^\infty \frac{k \sin(kr)}{\sqrt{1+v^2(k-k_F)^2}}dk
Let's assume that v kF >> 1, so that the the oscillating piece at large k doesn't contribute much uncertainty. Ideas? Thus far, Mathematica has...
Jhenrique, what the others aren't bothering to tell you is that your hypothesis is following the right line of intuition. The correct generalization of the fundamental theorem of Calculus to a two-dimensional integration across a rectangular region is given by
\iint \limits_{y_0 x_0}^{y_1...
Good point. I could be a little more creative with functional forms and still get around this, however. For example, Δk would still be smooth and continuous at the Brillouin zone boundary if it had the following form, wouldn't it?:
Δk = EkΔ0[cos(kx)-cos(ky)], with Ek=√[Δ02+ε2(k)]
ZapperZ, sorry, I'm still struggling for the right way to word this. I guess what I'm trying to ask is this: Let's assume that we have a dx2-y2 superconductor in a square-lattice crystal structure. (I'm imagining a cuprate superconductor, but it might not necessarily have to be the case)...
Thanks. As I understand it, Gorkov writes (see Eq. 15) that
ψGL(r) = Δ(r) * constant.
In the Scalapino reference, he writes that the "relative coordinate wave function ψ(x1-x2) describes the orbital symmetry of the pairs" and is given by
ψ(x1-x2) = ∑k ψk eik(x1-x2),
with ψk defined as in my...
Two questions, really:
I’m finding it hard to wrap my head around the connections between k-space and real-space for d-wave symmetry, as well as the connections between “order parameter,” “gap,” “Cooper pair wave function,” and “superconducting wavefunction,” which are all mentioned at various...