513.001 Molecular and Solid State Physics

Kittel problem 6.1

Show that the heat capacity of a monatomic lattice in one dimension in the Debye approximation is proportional to T/Θ for low temperatures T << Θ, where Θ is the effective Debye temperature in one dimension defined as 2πΘ = hω_m/k_B = hπv₀/k_Ba; here k_B is the Boltzmann constant and a the interatomic spacing.