# Questions tagged [density-of-states]

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### Density of states of Bogoliubov quasiparticles

For a simple fermionic system the formula for calculating the density of states (DOS) is $N(E) = \sum_{n}\delta(E-E_{n})$ where $\{E_{n}\}$ is the set of eigenvalues obtained after diagonalizing the ...
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### What does it mean to divide by the degeneracy of the state in this textbook excerpt?

This section of Griffiths Introduction to Quantum Mechanics deals with Boltzmann, Fermi-Dirac, and Bose-Einstein distributions. I don't understand this line (highlighted in yellow): Let's talk only ...
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### Photon density of states: Polarization/Helicity degree of freedom?

Sakurai's "Advanced Quantum Mechanics" states in Eq. (2.116) that the density of states of a single photon with $\vec k$ vector pointing into the solid angle $d\Omega$ is given by \begin{equation} \...
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### Density of phonon states from dispersion relation

I have a dispersion relation $$\omega( \textbf{q} ) = \omega_0 \sqrt{ \sum_{j=1}^{D} \sin^2{\frac{q_ja}{2}}. }$$ Where D is the dimension D=1,2,3. And my excersise is to calculate (numericaly on a ...
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### Passing from a discrete summation to a continous integal

I'm having trouble understanding the math behind a step in an explanation of BCS theory. At one point the superconductor gap $\Delta$ is defined as \begin{equation} 1 = V \sum_q \frac{1}{\xi_q^2+\...
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### Number of states $\Omega(E)$ derivation (Reif problem 2.4)

Problem 2.4 from Reif's "Fundamentals of Statistical and Thermal Physics": Consider an isolated system consisting of a large number $N$ of virtually non-interacting localized (not translating) ...
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### Density of states of 3D harmonic oscillator

Consider the following passage, via this image: 5.3.1 Density of states Almost all of the spin-polarized fermionic atoms that have been cooled to ultralow temperatures have been trapped by ...
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### Why do the high frequency waves have the most number of modes?

While reading the Wikipedia page of Ultraviolet Catastrophe, I came across how Rayleigh and Jeans applied the equipartition theorem. They told that each mode must have same energy. Now as the number ...
2answers
343 views

### How does the density of states for black-body radiation change with geometry?

If I have a hollow conducting cylinder with another conducting cylinder inside it (as with a coaxial cable), would the density of states of the photons/radiation between the two cylinders be any ...
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### Density of States vs Dispersion

I have a rather naive question regarding DOS and dispersion. We showed the existence of a band gap in class for a small, periodic perturbation in class last week. When drawing this, the professor ...
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### What methods exist to calculate the density of states in the continuum of a molecule?

Say I have an arbitrary molecule in the Born-Oppenheimer approximation, and furthermore say that I can approximate the molecule as having only one active electron. What methods exist to calculate the ...
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### Density of classical states in quantum theory

Let's first treat electrons as classical objects. I can evaluate the classical energy of each state in a configurational space (3N real numbers and, say, spins) using just Coulomb's law. Then I ...