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    I Importance of the energy gap in electronic transport properties

    current is e*v. What happens to v upon reflection?
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    I Importance of the energy gap in electronic transport properties

    If you studied chapter 9, then you know that free electron bands are parabolic and the weak potential introduces gaps at the BZ boundary. If these gaps are large, the electrons will remain in the same band in extended BZ. If the band gap are small, the electrons may end up in a higher band if...
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    I Importance of the energy gap in electronic transport properties

    Part of this we discussed in another thread. An electric field will drive the electrons through the band in k space. When they reach a zone boundary and there is a band gap, they get reflected to the opposite zone boundary. However, if there is no gap, the dynamics will be non-adiabatic and they...
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    A Berry curvature in solids

    Applying a spatially constant electric field to a charged particle will increase its momentum and k value. Including another gauge, namely V=eU=eEx, makes the spatial dependence explicit.
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    A Berry curvature in solids

    With a constant electric field ##E##, ##A(t) \sim Et##, so ##A## will be periodically equal to a reciprocal lattice vector ##G##.
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    A Berry curvature in solids

    Yes, the hamiltonian is periodic in k with period G. The question, how slow A(t) has to change with time is difficult and may differ for different states. It will usually hold if ## \langle i | (\partial H(t)/\partial t | j \rangle << | E_i(t)-E_j(t)| ## for all states i and j in question.
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    A Berry curvature in solids

    Well, the wavefunction of an electron in a periodic potential is of Bloch form: ##\psi_{kn}(x)=u_{kn}(x)\exp(ikx)##, where ##u_{kn}(x)## has the periodicity of the lattice. The hamiltonian, which has the ##u_{kn}## as eigenfunctions is ##H=\frac{1}{2m}(p-ik)^2+U(x)##, i.e., ##k## appears as a...
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    Doubt related to Drago's rule

    On a simple level, VSEPR theory comes to my mind.
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    Doubt related to Drago's rule

    Strangely enough, for at least 50 years now, no theoretical chemist believes any more in the geometry being dictated by hybridization. Yet teachers don't stop parroting this old lore.
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    Electron Configurations -- Why is terbium's electron configuration [Xe] 6s2 4f9 ?

    I would not consider f0, f7 and f14 as exceptions. Binding energy increases and size of f orbitals decreases continuously with increasing nuclear charge. So evidently f0 and f14 are extremal. After f7, orbitals have to be occupied with two electrons, which costs more energy. Also, while...
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    A Wannier function in tight-binding model

    Wannier functions are a kind of localized functions which evidently can also be calculated in a LCAO approach. So I don't think this is an alternative method of calculation, but rather representation. Note that the full wavefunction in Hartree Fock is invariant under arbitrary unitary...
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    Electron Configurations -- Why is terbium's electron configuration [Xe] 6s2 4f9 ?

    There are many factors influencing the precise electron configuration of the lanthanides and actinides, but there are some trends. The f-electrons are bad in screening each other from the nuclear charge, hence, the more f-electrons in an atom, the more tightly they are bound. On the other hand...
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    Chemistry Redox Reaction when a compound is both oxidized and reduced

    You are right! Of course it is possible to have the following two reactions ##\mathrm{OCl^- \rightarrow Cl^- + \frac{1}{2} O_2}## and ##\mathrm{H_2O_2 \rightarrow \frac{1}{2} O_2 + H_2O}##, which somehow autocatalyse each other. A possibility to distinguish the two possibilities is to use...
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    I Electron correlation vs electron exchange

    Let me add this: The most classical approximation to a many electron problem is via a Hartree product wavefunction. To get exchange symmetry, you have to consider all permutations and end up with a Slater matrix. This is the most general wavefunction describing somehow non-correlated electrons...
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    I Why are the d and f orbitals in transition metals considered localized?

    d and f orbitals are orbital in inner shells (n-1 and n-2, respectively), hence they are more localized in the inner of the atoms. The precise size depends also on the filling of the sub-shells. electrons in d- and f- orbitals hardly shield each other from the nuclear charge. Hence, as the...
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    MO labelling schemes

    There is the first sigma_g orbital, the second sigma_g orbital, the first sigma_u orbital, the second sigma_u orbital .... The symmetry is specified here by sigma/pi and the u/g label.
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    I Born-Oppenheimer approximations in molecules

    I doubt that is was considered a major breakthrough. The fact, that the electronic and nuclear motions decouple due to different masses and timescales was clear to most physicists and e.g. Slater published a paper with similar ideas already before Born and Oppenheimer. Nevertheless, the BO...
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    I Photons and wavelength in ultrafast optics

    Did you have a look at the article I cited in #5? It answers most questions on how photons with non-constant momentum can be defined.
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    B 2020 Nobel prize in physics

    I read the background paper by the Nobel committee and saw these beautyfull graphs of the star's position on an ellipse. What I was wondering: The black hole does not seem to be in one of the focal points, not even on the axis. On the other hand, I would have expected the rotation of the...
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    Calculate the bond-dissociation energies and entropy of a molecule

    You can do so using Quantum Chemistry programs like Gaussian: https://gaussian.com/
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    A Spin-orbital combination and the exclusion principle

    Just a side note: Just because two states have the same value of l, doesn't necessary mean that they are identical. E.g. a helium atom in a 1p^12p^1 state.
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    I Photons and wavelength in ultrafast optics

    That's absurd! Would you also say that e.g. an electron in a wavepacket has by necessity to be described as a superposition of electrons of definite energy?
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    Optical Build a ballast for an Osram Hg-Cd/10 spectral lamp

    Thank you, yes, I too found some more detailed information in the meantime. Finally, I decided to buy a used balast at ebay.
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    Reason for Ferroin's color shift

    The colour is mainly due not to d-d* transitions but due to charge transfer from the metal to the ligand.
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    What do I need for a home lab?

    Dear cats, maybe you might enjoy having a look at the golden book of chemistry. At least I like these kinds of books from a time when doing chemistry in a home lab was not considered a potential act of terrorism: https://sciencenotes.org/wp-content/uploads/2016/01/goldenbookchemistry.pdf...
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    A How are the thermal expansion of a solid and the stress tensor related?

    Sounds like you were interested in the Grüneisen relation.
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    I Photons and wavelength in ultrafast optics

    A photon does not have to have to be a momentum eigenstate. You can also have quite localized photon states: https://arxiv.org/pdf/0903.3712.pdf
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    What do I need for a home lab?

    Come on, there's also halal gelatine from cattle.
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    What do I need for a home lab?

    I had my own home lab as a teenager and studied chemistry afterwards. So I am very supportive of doing experiments at home. Basic ingredients are safety googles and the advice to never ever do pipetting by mouth. Instead of starting to set up an all pupose laboratory, I would rather recommend...
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    Optical Build a ballast for an Osram Hg-Cd/10 spectral lamp

    Thank you Dave, Be assured that I won't run for the next resistor. Meanwhile I found some documents which show that these ballasts aren't rocket science: http://dokspeicher.de/121006/Leybold-Spektrallampen-121006.pdf...
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