Density of states Definition and 149 Threads

Hi, I'm studying statistical mechanics from Reif's book. In his book Reif is reaching the conclusion that the number of states avaiable to a system at energy E (up to some small uncertainty in the energy due to finite observation) with f degrees of freedom is proportional to E^f . There is...

Homework Statement I am trying to retake an old course in statistical mechanics but run into integrals that i simply have forgotten how to solve. Given an denstiry of states such that f(\epsilon)= \frac{1}{|\epsilon |} for \epsilon_{min} \leq \epsilon < 0 and 0 elsewhere Using the mean...

I'm trying to get my head around the step function and the energy states of the quantum well. What I've got so far is this: The density of states for an electron confined in one direction by the potential barriers of the well, but free to move in the other two directions in the place of the...

Homework Statement I'm having a dumb moment in proving why the following is true: D(k)d3k=\frac{V}{4\pi^{3}}4\pi k^{2}dk Homework Equations NA The Attempt at a Solution I realize that the second part 4\pi k^{2}dk is an integration element d3k. But the density of states I can't...

I have seen thee following relation in regards to free electron waves with wavevector k : < k | k' > = (2.pi)^3 . d( k - k') where d() is a Dirac delta function. Why the 2.pi factor?? I can't seem to motivate it. Also, from this, it is stated that the density of states is then 1 /...

Homework Statement Consider a two-dimensional solid, such as a thin layer of mica or graphite. Assume the material can only vibrate in a direction perpendicular to its own plane, i.e., there is only one polarization. Find the density of states for the solid. Homework Equations for a...

I am having difficulty ascertaining the difference between an electrostatic charge present on the surface of a conductor and the flow of an electron current (or holes, if you prefer) along the surface of a conductor with respect to their effects on the electron density of states (and, more...

I need to calculate the density of states for a dispersion relation which is like the free electron dispersion, but with one effective mass in the kx, ky directions, and a different effective mass in kz. So I need to integrate the inverse gradient of E(k) over a surface of constant energy, ie...

After a fruitless search for a good undergraduate resource for Green's Functions (Economou's book is far too advanced for an intro course) , I hope someone here can clear this up. So I have the Greens Functions (gf) for the time independent Schrodinger equation: SUM |a><a| / (E - e(k))...

Hello everyone Lately I am taking some problem with my thesys, I am not an expert in theoretical physics but not bad as experimetal. I want to calculate the contribution of the w(q) away from zone O ob Brillouin to fit my experimental data to the theory and to know if the quantum theory work...

Hello everyone Lately I am taking some problem with my thesys, I am not an expert in theoretical physics but not bad as experimetal. I want to calculate the contribution of the w(q) away from zone O ob Brillouin to fit my experimental data to the theory and to know if the quantum theory work...

Hi there, I'm a bit confused as to the meaning of the following figure, for the quantum well case: I understand that with the quantum dot, since the states are completely quantised you get the delta functions - states only exist at certain energies so the DOS at these energies is non zero...

Homework Statement I'm having a little bit of trouble getting started with this problem. Can I get a little help? Using: (number of states in the six-dimensional region d^{3}x d^{3}3p) = (d^{3}x d^{3}p)/h^{3} Which provides a convenient route to the single-particle density of masses. a)...

Hello! I have a very simple question... Does anyone know if exists on the WWW a database where I can download the calculated density of states for the transition metals? I want data not just pictures! Thanks

Dear all, I am doing summer research in the field of Molecular Quantum Electro Dynamics, and a persistent problem that I (and occasionally the group I am working with) have/has is knowing what to use as the density of final states (radiation states). It is required in the Fermi Golden...

Homework Statement According to the non-relativistic quantum mechanics of a particle of mass m in a cubic box ov volume V = L3, the single particle energy levels are given by Ek=\hbar2k2/2m where k is the magnitude of the wavevector K = (kx,ky,kz) and where the components of k are...

regarding the density of states: how I GET THE FOLLOWING EQUALITY? \langle E_n\mid \delta(E-\widehat{H}) \mid E_n \rangle = \sum_n \delta(E-E_n)

Hi all. Is there any place where I can check how to derive the DOS of bilayer graphene subject to an external field. I have got the Hamiltonian right and solved the eenrgies but then I am not sure how to obtain the DOS right.. Thanks

Homework Statement I am trying to understand how we go about calculating the density of states in situations where the available quantum states are continuous, e.g. electrons in a white dwarf. I am happy to accept the uncertainty relation (we learned to derive it as the product of the...

Hi guys In some articles I've read, they all mention that the (local) density of states is related to the retarded Greens function for a non-interacting system by -(1/π)Im[G(r,ω)] = LDOS(r,ω), i.e. the imaginary part of the Greens function. The above relation holds because in k-space the...

Hi guys I have an analytical expression f(x) for my density of states, and I have plottet this. Now, I also have a complete list of my Hamiltonians eigenvalues. When I make a histogram of these eigenvalues, I thought that I should get an exact (non-continuous) copy of my plot of f(x). They...

Hi guys I found this on Google Books...

Homework Statement Consider an isolated system consisting of a large number N of very weakly interacting localized particles of spin 1/2. Each particle has a magnetic moment \mu which can point either parallel or antiparallel to an applied field H. The energy E of the system is then E =...

i have an equation for the density of states that depends on 1/(sqrt E). i have lots of coefficients to this [Vm^{3/2} w_c ] / [2 sqrt {2} pi^2 hbar^2] do these coefficients represent the degeneracy of the desity of states?

Hi. I'm studying the transition rates between a state a and a state b in the continuos level. In the book "Physics of atoms and molecules" by Bransden and Joachain it is said: We have to calculate the density of final states. To do this let the volume V be a cube of side L. We can impose...

Hi, I am trying to find an expression for the density of states of free two-dimensional electrons, as a function of energy, and I am really struggling. I get that what I am looking for is the number of states per unit area of k-space per unit energy, and in general (3D), this is expressed as...

Hi, I have a question about statistical mechanics. How do you calculate the density of states for phonons and electrons in a d-dimensional system (at fixed chemical potential) and when the dispersion relation for the electrons is E(p)=A |p|^g and for the phonons is w=v|p| To get the...

Hello, is it possible to roughly estimate the density of states just looking at the band structure E(k) of a solid? Thanks

Hi, I would like to know what local density of states (LDOS) is and what differences it has with projected density of states? Also, when we choose a smaller isolevel we have a denser local densities of states, why? Regrds,

Dear all, I really need help. My question: How do i project the density of states onto orbitals of atoms? this is to do a charge analysis. Can anyone provide me with an eqn or refer me to any relevant text or paper. Greatly apprieciate your help. Thanks nisha

calculate the density of states and average energy for an elctron gas in 1d,2d and 3d I know the number of states is N= \int_{0}^{infinity} g(e)f(e) de and E = \int_{0}^{infinity} g(e)ef(e) de and g(e) =dN/de

Hello, folks. Q: How can one measure the density of states of a semiconductor and a conductor? I would imagine you want to measure the charge carrier density and then you can calculate the density of states. If so, what observable(s) can yield the charge carrier density? How can you...

Homework Statement We study a one dimensional metal with length L at 0 K, and ignore the electron spin. Assume that the electrons do not interact with each other. The electron states are given by \psi(x) = \frac{1}{\sqrt{L}}exp(ikx), \psi(x) = \psi(x + L) \psi(x) = \psi(x + L) What is the...

Homework Statement We study a one dimensional metal with length L at 0 K, and ignore the electron spin. Assume that the electrons do not interact with each other. The electron states are given by \psi(x) = \frac{1}{\sqrt{L}}exp(ikx), \psi(x) = \psi(x + L) What is the density of...

"the density of states (DOS) of a system describes the number of states at each energy level that are available to be occupied. " But I thought there can't be more than 1 electron in a state? How does DoS have any meaning when dealing with eleectrons?

So we all know, or can look up Fermi's golden rule to be something like: \sigma\left(E\right) \propto \rho\left(E\right) |\langle \psi_i | \mu | \psi_f\left(E\right) \rangle|^2 Sigma is the cross section (or can be the transition rate as well), rho is the density of states of the final state...

[SOLVED] density of states for a Bose gas Homework Statement My book (Kittel) says that the density of states of an ideal Bose gas is:D(\epsilon) = V/4\pi^2 \left(2M/\hbar^2 \right)^{3/2} \epsilon^{1/2} I do not understand why the density of states is not identically infinity since the point...

condensed matter--integral over density of states Homework Statement http://online.physics.uiuc.edu/courses/phys460/fall06/handouts/460-lect12.pdf Could someone explain to me why the first equation on slide 22 is true? Homework Equations The Attempt at a Solution

Hi All Im just wondering if there is an easy way to determine the density of states for a molecule such as CO2. I am interested in transitions at IR wavelengths so I'm wondering if there is an 'easy' way to get at the vibrational modes only to chuck into something like the Maxwell-Boltzmann...

Hi, I have a question regarding the contribution of some molecular orbitals (e.g HOMO, LUMO) to the total density of states of a two-probe system. How exactly are the contributions of the MO ( that look similar to the DOS plots ) calculated, do they have something to do with the local...

If an infinite discrete sum is calculated via integrating over a density of states factor, is this integral an approximation to the discrete sum? i.e the discrete sums could be partition functions or Debye solids.

Hi! I want to calculate the density of states in the 3D, free electron gas, but I don't know how to do this. Can somebody help me? Thanks!

Although I have some major conceptual problems with the Fermi gas as treated in my solid state physics notes (see this thread: https://www.physicsforums.com/showthread.php?t=161222, I have attempted to solve this homework problem in an analogous manner to the solution for the 3D Fermi gas given...

Let's suppose we have a Phonon gas in 1-D then: - density of states g(k)=A/ \frac{ d\omega (k)}{dk} (i don't remember the value of constant A sorry.. :-p :-p ) - The Schroedinguer equation (NO interaction) would be: H_TOTAL =\Sum_{i}\frac{P^{2} _{i}}{2M}+ \sum_{i}B\omega ^{2}(k)...

Density of states?? According to C. Kittel the density of states is the "number of orbitals per unit energy range". Alright, that's fine, but what exactly does this mean? I can understand the calculations, finding the totalt number of states by considering the fermi sphere and the volume of a...

upon recent studies of the Density of states and Specific heat capacities, I've found the Einstien and Debye Models to be very helpful, Debye being the more accurate of the two models at low temperatures as it takes into account the low frequency modes. However, the realistic density of states...

what is the essentail difference between local density of states and density of state? It is very difficult to figure it out

The Density of States diagram gives gaps sometime. As I know, if the band is filled up to the gap, then the material is an insulator. However, it seems to me, that superconductors also open a gap in their density of states diagram, as BCS theory says. If my understanding is correct, I am a...

Dear all: I am frustrated in the concept of the PDOS, may someone be kind to refer me to the origin of this concept? Thanks. Regards