What is the density of state exactly?(STATISTICAL MECHANICS)

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SUMMARY

The density of states (DOS) in statistical mechanics quantifies the number of available energy states per unit volume within a specific energy interval, denoted as ΔE. In momentum phase space, the degeneracy factor is expressed as g = (V/B)dp_x dp_y dp_z, which transforms to g = (V/B)4πp² in polar coordinates, illustrating the relationship between momentum and energy states. This transformation indicates that the dp terms are integrated out when considering spherical coordinates, emphasizing the distinction between degeneracy and density of states. The discussion clarifies that DOS applies to systems such as gases, where energy levels are not discrete like those of individual atoms.

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  • Understanding of statistical mechanics concepts
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  • Knowledge of polar coordinates in physics
  • Basic grasp of energy states and their representation
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jessicaw
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Welcome just descirbe what is density of state and its physical meaning if you are tired of answering my more numerical question below!

My confusion mainly stems from this dilemaaa:
In momentum phase space:
weight(degeneracy) is:
[tex]g=\frac{V}{B}dp_{x}dp_{y}dp_{z}[/tex]

but suddenly the dp term vanishes in polar coordinates and becomes:

[tex]g=\frac{V}{B}4\pi p^2[/tex]
??

why the former has dp terms? Is degenracy equal to density of states in momentum space? Or is it a typo in my notes?
 
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