Thermodynamics, Statistical Physics, and Quantum Mechanics

222 SOLUTIONS

harmonicoscillator offrequency whoseenergylevels are

The average energy in the circuit is given by (with

The average energy is equally distributedbetween the capacitance and the

inductance:

where V is the voltage across the capacitor (between points A and B; see

FigureS.4.96). We then have

In the classical limit

We could equally well have derived the classical result by using the equipar-

tition theorem (see Problem4.42). For the single degree of freedom, there

is an average energy which, as noted, is divided between the capacitor

and inductor, so

a)

where is the charge on the capacitor. This is theHamiltonian of a