513.001 Molecular and Solid State Physics

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Kittel problem 6.1

Show that the heat capacity of a monoatomic 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 = hωm/kB = hπv0/kBa; here kB is the Boltzmann constant and a the interatomic spacing.