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

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SUMMARY

The discussion centers on the calculation of the density of states function in statistical physics, specifically addressing the transition from n-space to k-space. Participants clarify that k-space refers to momentum space, while n-space pertains to coordinate space. The integral over an eighth of a sphere in k-space is emphasized as essential for accurate calculations, despite the linear relationship between n and k, defined as n = (L/π)k. The conversation highlights the importance of understanding these concepts in both classical and quantum statistical mechanics.

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  • Basic concepts of classical and quantum mechanics
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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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