PHY3063 R. D. Field Department of Physics Chapter3_15.doc University of Florida Planck’s Theory (2) New Partition Function: The classical partition function must now be modified as follows: ∑∫∞=∞=→=00)()(nnplanckclassicalEPZdEEPZ, where Pn(E) is the Maxwell-Boltzmann distribution nhfEnAeAeEPnβ−−==)(. As before β= kT, but nowyAyyAAyZnnplanck−=+++==∑∞=1)1(20L,where hfey−=. Thus, hfplanckeAZ−−=1New Average Energy:As before )(logZddE−>=<, but now kTexhkTehcehfEhxxhakThckThfplanckaa→−=−=−=><>>1)/(1/1///λ,where xa= kTλ/chas dimensions of “action”(i.e.dimensions of h).Note that the average energy now depends on λand goes to zero as λ→0. For
This is the end of the preview. Sign up
access the rest of the document.