The problem statement, all variables and given/known data Analyze the specific heat of a one dimensional lattice of identical atoms: Show within Debye approximation that the specific heat at low temperatures ( ≪ Θ) is proportional to T/ΘD . Here ΘD=ℏD/ kB = ℏvs/KBa is the Debye temperature valid for 1D, kB the Boltzmann constant, a the lattice constant, vs the velocity of sound and D the Debye frequency. The attempt at a solution I know how to find out for a linear chain. But I do not know where to start in case of a 1-D lattice. please help.