Questions tagged [density-of-states]

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Density of States in NOT Free Electron Gas

I think that I understand how the density of states works for a free electron gas. It is effectively just a conversion factor between summing over values of k and integrating over values of E. If you ...
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3answers
6k views

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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0answers
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DOS of Van Hove singularity in 2D square lattice tight binding model

For the simplest example, 2D square lattice tight binding model gives the energy band as $$\varepsilon_k=-2t(\cos k_x+\cos k_y) \, .$$ We know that $\mathbf{k}=(0,\pi)$ and related momentum points are ...
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1answer
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Liouville's Theorem For Spacetime

Liouville's theorem states that the density of phase space governs the continuity equation. $$\frac{\partial\rho}{\partial t}+\sum_{i=1}^n\Big(\frac{\partial(\rho\dot{q_i})}{\partial q_i}+\frac{\...
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1answer
412 views

Getting the density of states for photons

I know that the density of states $g(\epsilon)d\epsilon$ is the number of states in the energy range $[\epsilon, \epsilon + d\epsilon]$. I considered a system of non-interacting free photons in 3 ...
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2k views

How to calcualte density of state from computed phonon dispersion?

I have numerically computed phonon dispersion using small displacement method by solving dynamical matrix along high symmetry direction [100], [110] and [111] for f.c.c lattice. Now I want to ...
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1answer
175 views

is it necessarily true that the partition function $Z$ (with degeneracies) $ =1$?

The partition function with degnerate energies is $$\text{Z}=\sum _ig_ie^{{-E_i}/{k_BT}}.$$ Because the partition function Z is defined as the normalisation constant, does Z always = 1?
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Fermi Dirac distribution and degenerate energy states

In Quantum Mechanics and in semiconductor materials, the number of electrons $N$ in conduction band is usually computed as follows: $$N = \int_{E_c}^{+\infty} g_c(E)f(E)dE$$ where $g_c(E)$ is the ...