2.10. Thermodynamics of one-dimensional oscillators Consider a set of N particles of mass m placed along a line of length L. Let pi and qi be their momentum and coordinate respecively. Their Hamiltonian is H =

N



i=1 p2i 2m

+ 1 2

k N−1



i=1

(qi −qi+1)2.

a. Determine the frequencies of the normal modes of the system.

b. Compute the partition function.