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

AI Thread Summary
Density of states (DOS) quantifies the number of available quantum states at a specific energy level within a given volume. In momentum space, the degeneracy factor incorporates differential momentum elements, which can change when transitioning to polar coordinates, leading to the appearance of the 4πp² term. This raises questions about whether degeneracy and density of states are equivalent in momentum space. The confusion also extends to the context of DOS in relation to atoms versus gases, as atoms have discrete energy levels while gases exhibit a continuum of states. Clarifying these concepts is essential for understanding the physical implications of density of states in statistical mechanics.
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:
g=\frac{V}{B}dp_{x}dp_{y}dp_{z}

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

g=\frac{V}{B}4\pi p^2
??

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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