# Phase space volume

## Main Question or Discussion Point

In calculating entropy in micro canonical ensemble we use KlnW where W is the no. of accessible micro states to the system , now when we move on to canonical ensemble ,we calculate the partition function and from there derive the thermodynamics of the system , and divide it by factor of h to make it dimensionless , now if one is asked to calculate phase space volume , it means we calculate the partition function by integration of exp[B(H(q,p))] dqdp and not dividing this by h . Is this correct ??

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In calculating entropy in micro canonical ensemble we use KlnW where W is the no. of accessible micro states to the system , now when we move on to canonical ensemble ,we calculate the partition function and from there derive the thermodynamics of the system , and divide it by factor of h to make it dimensionless , now if one is asked to calculate phase space volume , it means we calculate the partition function by integration of exp[B(H(q,p))] dqdp and not dividing this by h . Is this correct ??
I think that's correct, except the exponential should have a negative sign.

I think you should remember that the whole reason for dividing by "h" is because you are calculating something classically and want it to work quantum mechanically (it's not just a dimension thing). There is no such thing as an integral over dqdp in quantum mechanics (except in the path integral formalism) as you can't know both the position and momentum at the same time. So you coarse grain the phase space by a box of size "h" and hope this uncertainty in phase space gives you the correct classical answer.