Density of states Definition and 149 Threads

Hi. Look at the picture on 1:28 and 1:37 in this video: How is it possible that the fermi-level is between two energy bands? The fermi level is defined as the highest energy level that contains an electron 50% of the time, so how is it possible for the fermi level being in an area that is...

Dear All: I'm very confusing with the relationship between photonic local density of states and the field intensity. In thermal equilibrium, the field intensity should be proportional to the photon's number (or squared) and also be proportional to the local density of states. We know that this...

Hi all, In Charles Kittel (Introduction to Solid State Physics) He writes : U (Total Phonon Energy ) = Σk∑p((ħ*ωk,p)/((exp(ħ*ωk,p/τ))-1)) I understand this, but then he integrate over k and multiply by density of states : U (Total Phonon Energy ) = ∑p∫dω*Dp(ω)*((ħ*ωk,p)/((exp(ħ*ωk,p/τ))-1))...

In wien2k software of Dft how we came to know specific states like 3p 2s 4d etc peaks in total density of state of a compound.how we can relate TDOS with bandstructure.

Adopted from my lecture notes, found it a little fishy: Shouldn't ##\frac{dp}{dE} = \frac{E}{p}## given that ##p = \sqrt{E^2 - m^2}##. Then the relation should be instead: \frac{dp}{dE} = \frac{E}{p} = \frac{E}{\sqrt{E^2 - m^2}}

In my particles course, it says we will use Fermi's golden rule to work out rates. FGR is: Γ=2π|Mfi|ρ For the case of non-relativistic phase space, my notes say the density of states can be found as follows (pretty much word for word): Apply boundary conditions Wave-function vanishing at box...

Homework Statement (a) the density of k-states g(k) = L^2*k/2*Pi. (b) the density of states g(E) = L^2*m/Pi*h^2 (c)The density of states per area n2D(E)=m*/Pi*h^2 (d) Sketch a graph of n2D(E) vs E. (e) Calculate n2D(E) as a quantity. The questions don't have to be answered in full a...

In some quantum textbooks [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. (T(E)=C×DOS1(E)×DOS2(E), where C is constant). However, in Landauer transmission formula (without tunneling) the transmission depends on both DOS and...

I'm a beginner in quantum optics. I always become confusing when the material's refractive index is complex. This time is about the photonic density of states. We know that if the material is not absorbing or dissipative, meaning the refractive index is a real number, the local photonic density...

I've heard any many places that the density of states (DOS) can be determined from an x-ray photoelectron spectroscopy (XPS) spectrum. Perhaps someone more knowledgeable than me can explain how this is done, or can direct me to a good resource? Thanks!

Hello. I have been in contact with some papers that use DFT softwares for calculating properties of solids, nanoparticles, etc and a lot of them comes with colorfull plots of density of states. I know the density of states gives the number of electrons in the range of energy, but what I don't...

Definition/Summary This term most commonly refers to the number of quantum states having energy within a given small energy interval divided by that interval. Equations g(E)=\sum_{s}\delta(E-E_s) N=\int dE g(E) The "density of states" need not (but it most often does) refer...

It's known that the Density of States in 2D is given by, g_2(E)dE = \frac{a^2m}{\pi\hbar^2}dE The density of states in 1D and 3D are as follows, g_1(E)dE = \left(\frac{a}{\pi}\sqrt{\frac{2m}{\hbar^2}}\right)\frac{1}{\sqrt{E}}dE g_3(E)dE =...

Homework Statement Part (a): Plot fermi energy as a function of N Part (b): Derive the density of states and find its value Part (c): How many atoms reside at 20% of fermi energy? Estimate diameter of cloud Part (d): For the same atoms without spin, why is the cloud much smaller...

Homework Statement Calculate the single particle density of states for massless particles with dispersion E=h_bar ck for a 3D cube of volume V Homework Equations E=pc, p=E/c, dp=dE/c, d^3p = 4pi*p^2 dp k=sqrt(k_x^2+k_y^2+k_z^2) k_j = 2pi/L l_j (j=x,y,z) The Attempt at a Solution I...

Homework Statement Using the dispersion relation at the Dirac Point calculate the electron density of states for graphene in both the valence and conduction band. Homework Equations ρ = density of states = k2/pi2 The Attempt at a Solution I looked up what Dirac Points...

How can we define density of state in continuous energy? As the term energy state comes from quantum mechanics which deals with discrete energies. Thanks in advance

To take into account the density of states for an ideal gas, we first calculate it ignoring the spin. Then to take into account the spin for a system of electrons we put the number 2 for two spin directions. Why don't we do such this for a boson gas? For example if we have a gas of spin 1...

Homework Statement Find the density of states g(ε) for an ideal quantum gas of spinless particles in dimension d with dispersion relation  ε= α|p|s , where ε is the energy and p is the momentum of a particle. The gas is confined to a large box of side L (so V = Ld) with periodic boundary...

what do you mean by density of states ? can you please explain to it ?

For a free electron gas the procedure for determining the density of states is as follows. Apply periodic boundary conditions to the free electron waves over a cube of side L. This gives us that there is one state per volume 2\pi/L3=2\pi/V And from there we can find the number of states at a...

My book gives a treatment of this problem for crystal vibrations, but I don't really understand it. It says: There is one allowed value of K per volume (2\pi/L)3. But at the same time it has just shown that Kx,Ky,Kz can take values ±2\pi/L which would certainly lead to more combinations of...

Homework Statement I need some help with the following problem: Homework Equations ##\rho(k) dk = \frac{L}{\pi} dk## ##L=Na## ##\omega^2= \omega_m^2 \ sin^2 (qa/2)## The Attempt at a Solution The density of states is given by: ##g(\omega)= \rho (k) / \frac{dw}{dk}## Where...

For an electron gas generated in the inversion layer of a semiconductor interface, my book gives the conduction band density of states for the two dimensional electron gas as: ##g(E)=\frac{L^2m^*}{\hbar^2 \pi}## Where m* is the effective mass of the electron. I can't follow how this was...

Hello! I'm having my materialphysics exam in a few days, and looking some of the older exams I saw that there are many times questions about band structure and density of states. More specifically there might be a picture of some band structure plus the density of states, like this. Then...

Hi All! I am doing my Masters project on III-V Nitrides, my question is really a basic one. What are the localized states and what is meant by localization energy and degree of localization, also that excitons are localized to the tail state? Could you please give me an answer and guide...

Homework Statement Hey all, I am having trouble following some of the notes that my professor posted with regards to waves inside a blackbody; here is what he posted: (the part in bold is what I am just not understanding) "Inside the blackbody box, we need for the position of the walls...

In my text: The number of states per unit volume of the real space & the reciprocal space is given by 1 / (4∏³) No further explanation is given. How do you get to this 4∏³ And how come the density of states is the same in real space & reciprocal space? I think this is...

The formula for density of states in a free electron gas is g(E) = (3/2) (n/E_{F})\sqrt{E/E_F}. However, this looks like it has no direct dependence on temperature. It seems that only the probability of electron occupation of a state changes with temperature, not the number of states itself...

The density of states at the fermi energy is given by D(E_F)=(3/2)n/E_F I understand the density of states is the number of states per energy per unity volume, accounting for n/E_F. I don't understand how the 3/2 multiplying factor accounts for the volume?

Homework Statement What is the density of states g(E) for a quantum system having the energy levels: En=hv(n+1/2)1/2 ,where n is a positive integer? Homework Equations g(E) = \frac{d\zeta}{dE} \zeta= area under curve of constant energy\area per state The Attempt at a Solution...

Homework Statement Calculate the density of states if the radiation oscillators are confined to a square (i.e. in two dimensions).Homework Equations The Attempt at a Solution This was one of the questions for my Modern Physics class, (we recently covered blackbody radiation), although based on...

Hi all, I was deriving the free electron gas for practice in 1, 2, and 3 dimensions, and I started wondering why they have different dependencies on energies and what that means. I got: 1D: ##g(E) = \frac{1}{\pi\hbar} \sqrt{\frac{2m}{E}}## 2D: ##g(E) = \frac{m}{\pi\hbar^2}## 3D: ##g(E) =...

If one has already known the dispersion dataset, for example, for 2D crystal, we know the 1000*2000 dataset for E=E(k_x,k_y), How to find the density of states numerically?

I have a classic infinite, linear chain of atoms, each of mass m, each separated by a spring with spring constant b and equilibrium distance a between each adjacent one. I know from my textbook that the dispersion relationship you get for this is: \Omega(k) = 2\sqrt{\frac{b}{m}} |sin(ka/2)|...

While studying about k-points, etc. I came across the terms density of states. What is it's physical meaning. research papers often have DOS graphs in which they segregate s, p, d contributions and talk about fermi level etc. Is this DOS the same as the kohn-sham orbitals that are solved for in...

Homework Statement Determine the total number of energy states in silicon from the edge of the conduction band to Ec + kT for T = 300K. Homework Equations N = \intg(E)dE The Attempt at a Solution I'm pretty sure I know how to do this one. The only problem is, when I get to the...

Homework Statement It's easier to post a picture of the problem: Homework Equations In picture, and boson occupation number: \left\langle n_k \right\rangle = \frac{1}{e^{\beta E(k)} - 1} Where E is the energy of the state with k and \beta = 1/k_B T The Attempt at a Solution Goal: Find...

I am the point where i need to learn about Density of states, how to explain the concept and how to then calculate it for different systems, however I am unable to find any texts that really explain it on an introductory level. If anyone knows any sources or text that have a good introductory...

Homework Statement Consider a gas of non interacting electrons in two dimensions with electronic density n by unit of area and mass m. The gas forms a square of sides L. 1)Assume periodic boundary conditions, find the density of states by unit of area. 2)Find the Fermi energy in function of...

When you consider a electron L×L×L box, I think I understand how to derive the DOS-spectrum. Unfortunately, when a small change is made to the problem, I really don't understand what to do, so I probably don't understand the theory at all.. This is the question: Homework Statement Consider a...

Consider waves in a box. It is customary to calculate the density of states either by enforcing vanishing boundary conditions, then the wave numbers are k=\frac{n\pi}{L} and we take only positive k, or using periodic boundary conditions, in which case k=\frac{2n\pi}{L} and taking all wave...

Homework Statement density of states of photon gas is proportional to ... (a)E^1/2 (b)E (c)E^3/2 (d)E^2 Homework Equations i know the relation for density of states of electrons which is proportional to E^1/2. So far i was thinking that electrons and photons shares the same...

Dear all, My aim is to get the density of states (DOS) per unit area for monolayer (bilayer) graphene. I have done this using mathematica. I have set a sampling k grid with 22500 points and computed the expression: DOS=(1/Nk)*Ʃ δ(E-Ek) where the sum is over the k points in the reciprocal...

Density of States Derivation -urgent Homework Statement Homework Equations λ=h/Px (Px = x momentum) L/λ=nx The Attempt at a Solution A summarized derivation from the lecturer has proven to be problematic when revising: as same in xyz direction just cube one direction...

I know its number of states per unit energy but what happens in the case of continuous energy?

Homework Statement Consider an electron gas with a density of states given by D(e) = ae2. Here a is a constant. The Fermi energy is eF. a) We first consider the system at zero temperature. Compute the total number of electrons N and the groundstate energy E. Show that the average energy per...

Homework Statement I know how to derive the density of states for an ideal gas by using the energy equation: E_n = A*n^2, where A = (h_bar^2*pi^2)/(2mL^2) but what about for a 'photon gas'? Do I use the same energy equation as above, or the following: E_n = (h_bar*pi*c/L)*n...

Homework Statement 1. Find the density of orbitals (often called 'density of states') for a free electron gas in one dimension, in a box of length L. 2. Find the density of orbitals for a free electron gas in two dimensions, in a box with area A. Compare with the three dimensional case...

So the problem is following. The density of states in energy space (3D case) represents the number of states per unit volume per energy. This means that the unit is #(number of states)/(cm^3 eV). This result can be seen in many solid-state physics books. I am reading some articles where the...