That's a fun question. No, the density of states isn't neglected. But in the classical limit, the density of states can be treated as a smooth function, instead of having to count individual states. For a system with E ~ λ², like considered here, the density of states happens to be constant, as long as there is one degree of freedom. (It depends on the dimensionality though; it is g(E) ~ E² for three dimensions.)
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Is the density of state neglected as a result of classical limit?
That's a fun question.
No, the density of states isn't neglected. But in the classical limit, the density of states can be treated as a smooth function, instead of having to count individual states.
For a system with E ~ λ², like considered here, the density of states happens to be constant, as long as there is one degree of freedom. (It depends on the dimensionality though; it is g(E) ~ E² for three dimensions.)
@@PhysicalChemistry Thanks for that!