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

AI Thread Summary
The discussion centers on the rationale for calculating the density of states in k-space rather than n-space, despite a linear relationship between the two. Participants seek clarification on the definitions of n-space and k-space, questioning whether k-space refers to momentum space and n-space to coordinate space. The conversation also touches on the applicability of these concepts in classical versus quantum statistical mechanics. The integral over an eighth of a sphere in k-space is emphasized as a critical aspect of the calculation. Understanding these distinctions is essential for accurate density of states calculations in physics.
11thHeaven
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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 an eighth of a sphere in n-space?
 
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Could you be a bit more specific? By k-space do you mean momentum space? By n-space what do you mean then? q-space as in coordinate space? Are you talking classical statistical mechanics or quantum or both?
 

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