Let,s suppose we have in statistical physics /Kinetic theory of gases the "sum"...(adsbygoogle = window.adsbygoogle || []).push({});

[tex] Z(\beta)= \sum_{n} g(n)e^{-\beta E_n } [/tex]

Of course depending on the behavior of {E_n} the sum will be difficult to evaluate..my question is if from the classical or semiclassical point of view the approximation

[tex] Z(\beta)\sim \int_{R^2}dxdpe^{-\beta H(x,p)} [/tex]

Where H is the classical Hamiltonian of the system..will be accurate enough to extract conclussions about the behavior of the systme and calculate Thermodynamical quantities (Specific Heat Cp,Cv,F,G,H,S)..thanks-

Where the Hamiltonian is usually of the form [tex] H=p^2 +V(x) [/tex] so in the end we deal with integrals of the form:

[tex] \int_{-\infty}^{\infty}dxe^{-\beta V(x)} [/tex] so for T<<1 we could perform a "Saddle point method" or simpli Numerical Cuadrature methods...

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Difference between a sum and an integral

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**