# What is Density of states: Definition and 149 Discussions

In solid state physics and condensed matter physics, the density of states (DOS) of a system describes the proportion of states that are to be occupied by the system at each energy. The density of states is defined as

D
(
E
)
=
N
(
E
)

/

V

{\displaystyle D(E)=N(E)/V}
, where

N
(
E
)
δ
E

{\displaystyle N(E)\delta E}
is the number of states in the system of volume

V

{\displaystyle V}
whose energies lie in the range from

E

{\displaystyle E}
to

E
+
δ
E

{\displaystyle E+\delta E}
. It is mathematically represented as a distribution by a probability density function, and it is generally an average over the space and time domains of the various states occupied by the system. The density of states is directly related to the dispersion relations of the properties of the system. High DOS at a specific energy level means that many states are available for occupation.
Generally, the density of states of matter is continuous. In isolated systems however, such as atoms or molecules in the gas phase, the density distribution is discrete, like a spectral density. Local variations, most often due to distortions of the original system, are often referred to as local densities of states (LDOSs).

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Hi guys. I want some help understanding how I can make the normalization of the JDoS density of states (Ω[E,m]) in the Wang-Landau algorithm. When I am working with DoS (Ω[E]) I use the knowledge that the value of the density of states in the ground states must be equal to Q (Q = 2 for the...
2. ### A Can I calculate partial density of states using tight binding?

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3. ### Phonon Density of States (PDOS) at Gamma Point

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14. ### I Where did the extra 8 come from in the derivation for density of states?

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15. ### Relationship between k and E when deriving the density of states

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16. ### Volume integral over a gradient (quantum mechanics)

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19. ### I Do Simple 2D Ising Models Have Constant Density of States?

Do simple 2D Ising models have constant density of states? How is it calculated?
20. ### I Density of States: 1-Dim Linear Phonons & Electrons Differences

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21. ### I Density of States -- alternative derivation

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22. ### A Localized states and density of states

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23. ### I 1D Phonon density of state derivation

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24. ### Calculating 3D Density of States for a Dispersion Relation | Homework Solution

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25. ### I Density of states at Fermi level for metal vs semiconductor

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26. ### I Why do we calculate the density of states using k-space?

In statistical physics the calculation to obtain the density of states function seems to involve an integral over an eighth of a sphere in k-space. But why do we bother moving from n-space to k-space, if there's a linear relation between n and k i.e. n = (L/π)k ? Why don't we just integrate over...
27. ### I Density of states with delta function

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29. ### I Number of electrons in conduction band

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30. ### I Density of states from 3D to 2D

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31. ### I Fermi sphere and density of states

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32. ### A Fermi energy Ef changes with applied electric field?

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33. ### Momentum density of states for pion decay.

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34. ### How to change density of states to eV

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35. ### Density of states, and integral of the Sommerfeld type

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36. ### How does doping affect the degeneracy of semiconductors?

Hello, I am new to the forum, so I am directly stating my questions. 1)What determines the density of states of Phonons in a semiconductor? 2)Does degeneracy of semiconductors depend only on doping? Thanks
37. ### Surface States within band gap STM/STS

Hi there people! So my question is why you can see localized surface states within the band gap of the material with an STM. How is a tunneling circuit being established?
38. ### Density of states in Fermi's golden rule

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39. ### Density of Energy Levels - Strange Summation

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40. ### Relation between electronic band structure and Fermi energy

I have some qualitative questions about the relation between band structure, density of states, and Fermi energy (or Fermi level). 1) Say you have a given electronic band structure (energy as a function of k) obtained by any method. How do you relate this to the Fermi energy (or Fermi level) ...
41. ### Volume Density of states (electrons)

Homework Statement a)Find the densities of states 0.08 eV above the conduction band edge and 0.08 eV below the valence band edge for germanium. Be careful with units and be sure to give the units for your answer. b) Find the volume density of states (i.e. number of states per unit volume)...
42. ### How to find the density of states from IV plot.

Is there any way to find the density of states from the IV graph
43. ### Density of States of a metal at Fermi level

Why can not the density of states of a metal at Fermi level be zero? Thanks!
44. ### What is the derivation for the vacuum density of states in the Purcell effect?

The Purcell effect is when an atom placed inside a high finesse cavity with a very small mode volume gets an increase in the spontaneous emission rate. I've tried to find correct explanation for this effect, but it seems hard to find, except that it comes from an increase in the vacuum density...
45. ### Having trouble with Density of States

I need to find the total number of states in a 1D monatomic lattice using the density of state equation g(ω), and I am having a hard time doing so. I'm fairly certain all I need to do ins integrate it, but this is proving to be a greater challenge than I thought it would...
46. ### Green's function and density of states

Dear all, In his book chapter " Green’s Function Methods for Phonon Transport Through Nano-Contacts", Mingo arrives at the Green's function for the end atom of a one dimensional lattice chain (each atom modeled as a mass connected to neighbouring atoms through springs). He gives the green...
47. ### Density of states in 2 dimensional box

I am trying to calculate the density of energy states in a two dimensional box. The way my professor did this is by first calculating the amount of states with their energy less than some energy e and taking its derivative with respect to e. In order to see how many energy states there are with...
48. ### Density of states of photonic crystal

Hello! Does anybody know how to calculate the DOS as a function of Neff and λ/Λ? Thanks.
49. ### Density of states, photonic crystal

Hello! I know how to calculate band structure and density of states of photonic crystal (example is pic.1) Does anybody know how to plot such DOS maps? The second picture is from the article about photonic crystal fibers by Rodrigo Amezcua.
50. ### Trouble understanding definition of density of states

According to my thermo textbook the density of states should really be called the density of orbitals because "it refers to the solutions of a one particle problem and not to the states of the N particle system". This makes perfect sense to me but now I'm confused about references to the density...