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Advanced PhysicsQ&A LibraryIn lecture we derived the canonical partition function QN(V,N) for the idea gas using a factorization method. One can also directly compute itby taking the Laplace transform of the microcanonical partition function Q(E,V,N). Using our result from lecture,Q(E,V,N) = [3 (2TME)3/2 ]N[(3N/2) - 1]! N!(Δ/Ε)compute directly the Laplace transform,QN(T,V) = |dEA Q(E,V,N)e-BEand show that you get the same result for QN(T,V) as found in lecture using the factorization method.Question

Asked Mar 2, 2020

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It's a statistical mechanics question.

Step 1

Write the microcanonical partition function *Ω*(*E,V,N*) and take the Laplace transform of it.

Substitute the expression given for *Ω*(*E,V,N*) in the above equation.

Step 2

Use the gamma integral and gamma function property to calculate the above integral, i.e.,

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