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    MATLAB Extract elements from a cell

    For future reference, when performing a uniform operation on arrays inside of a cell, just write a function to perform your desired task and have it operate across the cell using cellfun. For your current problem it would look like this: cellfun(@(f)f(1,2), a)
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    I Why are there not more ferromagnetic Materials?

    To begin, your quote from an unnamed source speaks of the "spherical symmetry of the environment" which you then took upon yourself to recast as "spherical movement of an electron" (a statement that is problematic in and of itself, but one that I am not going to address.) If we focus on what the...
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    A Electronic band structure of iron superconductor BaFe2As2

    As general rule, it is not very reasonable to expect that atoms, when condensed into a material, will follow a simple Hund's filling. Here is an article on the 122 pnictides that includes both theory and experiment that demonstrate the important role of correlations in establishing the...
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    I Molecular vibrations

    When atoms condense into a solid, then, as TeethWhitener pointed out, the primary modes are acoustic and optical phonons. These are vibrations that move as a wave through the material, ie: they are collective modes due to long range coordination of the atoms. In fact, they are guaranteed to...
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    Transmission of a thin film fitting using the Swanepoel method in MATLAB isn't working

    They clearly have a typo in their definition of C since there are two opening parenthesis, but only one closing. My guess is that it should be ##2(n^2 - 1)(n^2 - s^2)##. Try that and see if it fixes the problem.
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    A What is the mean inner potential in an ideal crystal of finite size?

    As I stated above, the paper I recommended works out the potential for you cubic system in the first half. The second half then works out the energy level scheme due to splitting the orbital degeneracy of electrons placed within this crystal field. So there is no simpler model, just disregard...
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    A What is the mean inner potential in an ideal crystal of finite size?

    What you are describing is Crystal Field Theory. There is extensive literature on this and the associated energy splitting of electron orbital degeneracy within these crystalline electric fields, ie: CEF levels. In general, the number of levels is determined by the local point group symmetry of...
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    A How to calculate density of states (DOS) from 8 energy eigenvalues of a Quantum model calculated by exact diagonalization?

    In my last post I said you needed to determine the interval ##dE## that matches ##dN=1##. If you are sitting at an energy interval in between two levels it should be abundantly clear that ##dN=0##. So for ##dE<(E_{n+1} - E_{n-1})##, would you agree with the following statement? $$ dN =...
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    A How to calculate density of states (DOS) from 8 energy eigenvalues of a Quantum model calculated by exact diagonalization?

    If there is no degeneracy then clearly ##dN = 1##, but if you need more detail then here it is. Your density of states is give by: $$D(E_{n}) = \frac{dN}{dE}$$ where ##N(E_{n})## is the total number of states up to energy ##E_{n}##: $$N(E_{n}) = \sum_{k=0}^n g_{k}$$ As you stated there is no...
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    A How to calculate density of states (DOS) from 8 energy eigenvalues of a Quantum model calculated by exact diagonalization?

    I assume you have also determined the degeneracy of the energy levels. With that in hand it you should be ready to determine the DOS by the standard prescription.
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    I Why XRD peaks are so sharp?

    Kittel "Intro to Solid State" has a simple exercise to walk you through demonstrating this yourself. It is problem 4 at the end of chapter 3. Assuming you have a copy, then you can work this out yourself. I will abbreviate this exercise even further to provide an immediate answer and a bit of...
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    Challenge Math Challenge - May 2019

    Attempt at Problem 4 Part a) follows directly from the fundamental property of self adjoint operators. $$ (\hat T{\mathbf a})\cdot{\mathbf b} = {\mathbf a}\cdot(\hat T{\mathbf b})$$ where ##\hat T## is a self-adjoint linear operator and ##{\mathbf a},{\mathbf b}## are two vectors in a given...
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    I Taylor Series for Potential in Crystals

    The answer as to why we do a Taylor expansion at all is because physics is hard. Indeed, for the Lennard Jones potential we use to describe lattice dynamics exact solutions are altogether intractable. So we do what we typically do with potentials in such cases, we Taylor expand around the...
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    I Haldane model trouble

    Previous thread with link to fantastic article:
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    I forgot the name of a theory in Magnetism

    Could you provide a bit more detail? What do you mean by two sources, and what generates the field? The closest match that comes to mind is the Kondo effect (starts with K) and has two 'sources' in the form of localized moments (electrons bound to specific atoms) and itinerant moments...
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    A Raman spectroscopy and the phonon confined in the Brillouin zone

    Raman is effectively a q=0 probe. The photon cannot impart enough momentum to study phonon processes along the full dispersion curve, you need inelastic x-ray or neutron scattering to do that.
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    Challenge Math Challenge - April 2019

    Could you give an example of (or clarify) this? Given that you speak of 'smaller and smaller spikes', this lead me to believe that the limit at infinity is still zero, such as in the classic example of a sine wave in an exponentially decaying envelope: $$ \lim_{n \rightarrow \infty}e^{-x}sin(x)...
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    Challenge Math Challenge - April 2019

    Thanks for catching that, I don't know why I left off the other term. It only makes my proof a bit longer. I also cleaned up my notation for the integral limits to make it more clear. I edited my original post to reflect these changes. Let me know if you see any other glaring mistakes.
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    Challenge Math Challenge - April 2019

    Solution to 4
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    Challenge Math Challenge - April 2019

    Again, thanks for catching an error. The last sentence has been removed. It was extraneous anyways. I also rephrased some of my reasoning for clarity. Cheers
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    Challenge Math Challenge - April 2019

    Ahhhh, there were some number typos in my original post. I have fixed them. Let me know if that clears it up.
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    Challenge Math Challenge - April 2019

    Solution to problem 1
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    A Powder XRD sample prep question

    Perhaps reaction with the environment or maybe the chemical treatment operates over different time scales. Either could result in breaking down or modifying the chemical structure which would result in a different peak structure. Can you leave the sample on the XRD machine and remeasure over...
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    I Quantized vortices in superfluid

    Begin by writing the density of your superfluid condensate in terms of its normalized macroscopic wave function $$n_{0}(\mathbf r) = \left|\psi_{0}(\mathbf r)\right|^{2}$$ In general the wave function is complex, so we can write $$\psi_{0}(\mathbf r) = \sqrt{n_{0}(\mathbf...
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    A Fermi gas in a magnetic Field?

    To know the total magnetic field requires calculating the magnetic susceptibility of the material, in this case that 'material' is a Fermi gas. The magnetic response of a fermi gas (ie: no correlations between electrons) in the presence of a magnetic field is well known. It will consist of two...
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    I Neutron Temperature

    Yes neutrons have a temperature. For non-relativistic free neutrons (eg: moderated neutrons radiating from a nuclear reactor) the equations are trivial ##E = \frac{3}{2}k_{B}T## where ##E## is the kinetic energy ##E = \frac{1}{2}mv^{2}##. Indeed, at neutron scattering facilities dedicated to...
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    I Database for magnetism and properties

    There is the ICSD that contains around 200,000 different crystal structures This is an extremely valuable database and is used all the time by researchers. However, this impressive database is due to the fact that they pay people to scour journals and...
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    I Understanding the Seebeck effect

    A simple harmonic oscillator has a force ##F = -kx## with the steady state solution ##x = A\cos(\sqrt{k/m} t)##. Thus, the time average is $$\bar F = \lim_{t_{f} \rightarrow \infty} \frac{\int_0^{t_{f}}-Ak\cos(\sqrt{\frac{k}{m}} t)\, dt}{t_{f} - 0} = -\sqrt{mk}\lim_{t_{f} \rightarrow...
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    I What causes magnetism at the atomic level?

    There is a lot to unpack here given that magnetism in condensed matter is a complicated subject. However, I will step through your post and try to provide an outline for properly working through this. The important thing to note here is that you are talking about a SINGLE atom and effectively...
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    A Solid-liquid critical point

    Here is a very recent paper outlining the melting of a skyrmion lattice via an intermediate hexatic phase in the material Cu##_{2}##OSeO##_{3}##. It touches directly on many of the things king vitamin detailed.