Thermodynamics, Statistical Physics, and Quantum Mechanics

140

numeratorequals zero. If is one of the then by theassumption ofU

infinite, the term still equals zero. Finally, if then by l’Hôpital’s

rule the first term again gives zero. In the second term, so

the expression reduces to

Finally,

d) By definition,

Given a polynomial dependence of the energy on the generalized coordinate:

(S.4.42.11) yields

To satisfy theequipartition theorem:

Thus, we should have

SOLUTIONS