Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 221

where we substituted from (S.4.95.9). Note that even modes do not

contribute to the fluctuation of the midpoint of the wire, as expected from

elementaryconsiderations. We may then find the fluctuation:

where we haveused the sum given in theproblem

So,

as before.

4.96 LC Voltage Noise (MIT, Chicago)

Write the HamiltonianHfor the circuit: