Thermodynamics, Statistical Physics, and Quantum Mechanics

We proceed to find

Thus, the result is the same by both approaches.

5.17 Coupled Oscillators (MIT)

The Hamiltonian of the system is

The problem is easily solved in center-of-mass coordinates. So define

These new coordinates are used to rewrite the Hamiltonian. It now decou-
ples into separate and parts:

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