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

In summary, the conversation discusses the concept of density of state and its physical meaning in momentum phase space. The speaker is confused about the presence of dp terms in the formula for degeneracy and the difference between degeneracy and density of states in momentum space. They also question whether the concept applies to gas or atoms, and provide a link for further understanding.
  • #1
jessicaw
56
0
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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  • #2

1. What is the definition of density of states in statistical mechanics?

The density of states is a concept in statistical mechanics that represents the number of energy states available to a system at a given energy level. It is a measure of the number of quantum states that can be occupied by particles in a specific energy range.

2. How is the density of states related to the energy levels of a system?

The density of states is directly proportional to the number of energy levels in a system. This means that the higher the energy levels, the higher the density of states will be.

3. What is the importance of the density of states in statistical mechanics?

The density of states is a crucial concept in statistical mechanics as it helps us understand the distribution of energy among particles in a system. It also allows us to calculate thermodynamic properties such as entropy and specific heat capacity.

4. How is the density of states calculated for a given system?

The density of states can be calculated using the formula: D(E) = (1/h^3) * V * (2πm)^3/2 * (E)^(1/2), where h is the Planck's constant, V is the volume of the system, m is the particle mass, and E is the energy level.

5. Can the density of states change for a given system?

Yes, the density of states can change for a given system depending on the temperature, pressure, and other external factors. It can also vary for different types of particles, such as fermions and bosons, due to their different quantum behavior.

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