# Questions tagged [density-of-states]

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### Degeneracy of Photons

The density of states for a photon gas is defined by, $$D(\epsilon)=\frac{g}{2\pi^2}\frac{\epsilon^2}{(\hbar c)^2}$$ where g is the number of independent internal states for a photon. The question is ...
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### Motivation for density of states

I have not found a good book on statistical mechanics that explains the quantity density of states well. The books I have read so far make the continuum limit approximation, which does not make much ...
1 vote
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### Density of states of a finite potential well

Considering a finite square potential well. The solution of it gives the isolated bound states (below zero) and continuous scattering states (above zero). Here the isolated and continuous are the ...
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### What is "Density of States" and how does one generally find it?

I'm walking out of a graduate quantum midterm kicking myself because I was asked to compute density of states as a function of energy for a spin $1/2$ particle of mass $m$ in a hard wall box of length ...
1 vote
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### Density of states: Ashcroft Mermin, Chapter 9 question no2

Ashcroft Mermin chapter 9 number 2 Hey, I'm just sutck on the problem 2 of the Ashcroft Mermin. I did prove the density of state but I'm having a hard time finding $k_\text{min}$ and $k_\text{max}$ (...
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### Justification and interpretation of Fermi Golden Rule (second order) in Resonance Energy Transfer (RET)

I hope someone can give me some new insight to understand this. Fermi's golden rule is wildly used to calculate the rate for RET. I have some difficulties in understanding its justification and ...
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### Density of states in microcanonical ensemble for discrete and continuum energy spectrum

I'm introducing myself to statistical mechanics using two books: Introduction to Statistical Physics by S. Salinas, and Statistical Physics of Particles, by Mehran Kardar. Both textbooks work on an ...
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### Derivation of Density of states in 3D

In our lecture today, the professor introduced the concept of density of states. We found the expression of it, for the 3D case, but no steps were shown and also we did not specify the system at hand ...
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### Average electron density of a Free electron gas

I'm trying to solve solving an exercise in quantum mechanics, and began facing some confusion regarding the definition of average electron density. For a 2D free electron gas, under an open boundary ...
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### How could one "empirically" calculate density of states?

I've been studying statistical mechanics and recently came across an interesting optional challenge. The Einstein model and the Debye model of solids are common ways of describing the heat capacities ...
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### Phase space density for Bose-Einstein condensation

A figure of merit for Bose-Einstein condensation is the phase space density which can be defined as $$\rho=n\lambda_T^3,$$ where $n$ is the number density of atoms and $\lambda_T$ the thermal de ...
1 vote
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### Going from 2D dispersion relation to density of states

If one was to have a 2D dispersion say: $$\varepsilon(k)=k_x^2-k_y^2$$ We know the dispersion relation generally can be written as:$$D(\varepsilon)=\sum_{k_x}\sum_{k_y}\delta(E-\varepsilon(k_x,k_y)$$ ...
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### Counting the number of allowed energy states of a particle in a 3D box

I am reading a book on Modern Physics by Thornton and Rex. I am looking at a particle in a 3-dimensional infinite square well potential (particle in a box). If the particle is a photon, its energy can ...
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### Single particle density of states for non-free particle

I am trying to find the single particle density of states in terms of the energy, for a system with the single particle 2D Hamiltonian: $$H=\frac{p^2}{2 m}+\alpha x \text { with } 0<y<L, x>0$$...
1 vote
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### Partition Function from Dispersion Relation in Molecular Dynamics

I’ve seen there are ways to compute the dispersion relation of a crystal from molecular dynamics. An example of how to do this is discussed in this question: Computing phonon dispersion from molecular ...
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### Average value of energy in statistical mechanics

I haven't taken any classes in Statistical Mechanics, but in studying Structure of Matter I found some ideas I'm not very familiar with, related with the average value of energy ($E$). Given a $p(E)$ ...
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### How can the total number of particles can be sum over all Density of states?

It is known that Density of states of a lattice structure is the probability distribution function of energy (for reference). This means that the sum/Integral of DOS over all energies is $1$. However, ...
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### Why is the conductance of a metal-insulator-metal tunnel junction parabolic?

For bias voltages below the tunnel junction barrier heights (and below the Fowler-Nordheim limit), tunnel junctions have a parabolic conductance as a function of bias. Is this due to the metallic ...
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### Density of states misunderstanding in Statistical Mechanics

In the simple model of a box filled with an ideal gas, one may write the total energy as the sum of kinetic energies of all particles $$E = \sum_{i=1}^N\frac{\vec{p}_i^2}{2m}$$ and so if you construct ...
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### DOS of swave superconductor for nonzero chemical potential and existence of Andreev bound state

I keep getting something, which I thought was wrong, but now I am thinking maybe not. The issue I am dealing with has to do with the DOS and a nonzero $\mu$. To begin let's note that the peak found in ...
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### Isothermal Gruneisen parameter for Germanium?

If phonon density of states peak shifts are purely quasiharmonic, we have $\omega$(V(T)). If phonon density of states peak shifts shifts are purely anharmonic, we have $\omega$(T). Does anyone know if ...
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### Recent review on high density equation of state?

Can anyone suggest a recent review on the equation of state of the matter at high (nuclear and above) densities? I would like this review to contain both astrophysical applications, mainly for neutron ...
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### Relation between critical temperature and density of states

The BCS theory predicts that the critical temperature of the superconducting transition is given by $$T_c \approx \theta \exp \left (- \frac{1}{U D(\epsilon_F)} \right )$$ where $\theta$ is the ...
1 vote
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### Double and triple sum into integral with density of states

I asked this on mathematical forum section. I'm triying to expand the results of certain calculation, where the author has the following kind of sums: $$\sum_{j} A(\omega_j) n(\omega_j),$$ where $A$ ...
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### Normalization of phonon density of states

Analogous to electronic structure calculations, we can solve for dispersion band structure of phonons for lattices using harmonic lattice approx. And we can find the so-called phonon density of states ...
1 vote
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### Canonical ensemble: what if the phase space density is not known?

In canonical ensemble, the probability is defined as \begin{equation} P(E)=\frac{g(E)\exp(-E/T)}{Z}, \end{equation} and the partition function is defined as \begin{equation} Z(T)=\int_0^{\infty}dE\,g(...
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### Density of states of one classical harmonic oscillator

I have to determine the density of states of one tridimensional harmonic oscillator. I have to prove that the expression is the following $D(E) = aE^2$, a is a constant. I know this is a 6-dimensional ...
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### Longitudinal conductivity from density of states (DOS)

It is well-known that using the so-called Streda formula, the transversal conductivity $\sigma_{xy}$ and thus the Hall conductivity in a two-dimensional material is given as the derivative of the ...
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### The range of velocity in Maxwell Velocity Distribution [closed]

If we see the formula for velocity distributions in x,y, and z-direction their range of velocity goes from -infinity to +infinity but when we take the whole velocity distribution, the range goes from ...
The question I have is how would I go about finding the density of states $\frac{dn}{dE}$ of an electron in a 1D infinite potential well with a width of $a$? I'm only just starting my quantum physics ...
What will the density of states be if the particle inside the 3d potential well is a spin 1 particle? \psi(x,y,z)_{n_x,n_y,n_z}= \left(\frac{2}{L}\right)^{3/2} \sin\left(\frac{n_x\pi x}{L}\right)\...