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)
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...
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...
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...
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.
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...
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...
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?
$$
dN =...
If there is no degeneracy then clearly ##dN = 1##, but if you need more detail then here it is.
Your density of states is give by:
$$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}$$
As you stated there is no...
I assume you have also determined the degeneracy of the energy levels. With that in hand it you should be ready to determine the DOS by the standard prescription.
Kittel "Intro to Solid State" has a simple exercise to walk you through demonstrating this yourself. It is problem 4 at the end of chapter 3. Assuming you have a copy, then you can work this out yourself. I will abbreviate this exercise even further to provide an immediate answer and a bit of...
Attempt at Problem 4
Part a) follows directly from the fundamental property of self adjoint operators.
$$ (\hat T{\mathbf a})\cdot{\mathbf b} = {\mathbf a}\cdot(\hat T{\mathbf b})$$
where ##\hat T## is a self-adjoint linear operator and ##{\mathbf a},{\mathbf b}## are two vectors in a given...
The answer as to why we do a Taylor expansion at all is because physics is hard. Indeed, for the Lennard Jones potential we use to describe lattice dynamics exact solutions are altogether intractable. So we do what we typically do with potentials in such cases, we Taylor expand around the...
Could you provide a bit more detail? What do you mean by two sources, and what generates the field? The closest match that comes to mind is the Kondo effect (starts with K) and has two 'sources' in the form of localized moments (electrons bound to specific atoms) and itinerant moments...
Raman is effectively a q=0 probe. The photon cannot impart enough momentum to study phonon processes along the full dispersion curve, you need inelastic x-ray or neutron scattering to do that.
Could you give an example of (or clarify) this? Given that you speak of 'smaller and smaller spikes', this lead me to believe that the limit at infinity is still zero, such as in the classic example of a sine wave in an exponentially decaying envelope:
$$ \lim_{n \rightarrow \infty}e^{-x}sin(x)...
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.
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
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...
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
$$\psi_{0}(\mathbf r) = \sqrt{n_{0}(\mathbf...
To know the total magnetic field requires calculating the magnetic susceptibility of the material, in this case that 'material' is a Fermi gas. The magnetic response of a fermi gas (ie: no correlations between electrons) in the presence of a magnetic field is well known. It will consist of two...
Yes neutrons have a temperature. For non-relativistic free neutrons (eg: moderated neutrons radiating from a nuclear reactor) the equations are trivial ##E = \frac{3}{2}k_{B}T## where ##E## is the kinetic energy ##E = \frac{1}{2}mv^{2}##. Indeed, at neutron scattering facilities dedicated to...
There is the ICSD that contains around 200,000 different crystal structures http://www2.fiz-karlsruhe.de/icsd_home.html
This is an extremely valuable database and is used all the time by researchers. However, this impressive database is due to the fact that they pay people to scour journals and...
A simple harmonic oscillator has a force ##F = -kx## with the steady state solution ##x = A\cos(\sqrt{k/m} t)##. Thus, the time average is $$\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...
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...
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.
https://arxiv.org/pdf/1807.08352.pdf