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    In an infinite quantum well, why Δn=0?

    Thanks, this ought to help.
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    In an infinite quantum well, why Δn=0?

    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...
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    In an infinite quantum well, why Δn=0?

    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...
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    What defines a polaron?

    Thanks to you both. These comments are helpful.
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    What defines a polaron?

    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...
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    What is the momentum of a hole in a semiconductor?

    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...
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    What is the momentum of a hole in a semiconductor?

    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...
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    Who is this "Kallen" and what does he represent, anyway?

    Thanks! Both these responses were helpful.
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    Who is this "Kallen" and what does he represent, anyway?

    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...
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    Brillouin Zone Confusion

    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...
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    Can one electron decay into an electron plus a phonon?

    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...
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    Can one electron decay into an electron plus a phonon?

    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?
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    Can one electron decay into an electron plus a phonon?

    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...
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    Can one electron decay into an electron plus a phonon?

    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...
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    D-wave superconductivity: Functional forms?

    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 ;)
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    Is there a conservation law associated with C4 symmetry?

    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...
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    D-wave superconductivity: Functional forms?

    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...
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    Questions regarding the Fermi level of a metal

    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"...
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    D-wave superconductivity: Functional forms?

    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)]
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    D-wave superconductivity: Functional forms?

    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)...
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    D-wave superconductivity: Functional forms?

    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...
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    D-wave superconductivity: Functional forms?

    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...
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