Hi! I feel like I've understood none of this stuff! A 1D chain of springs and masses modeling a chain of atoms has a dispersion relation ala ## \omega## ~ ##|sin(k a /2) |##, where ##k## is the wave vector and ##a## the distance between atoms. As far as I have understood, the debye model (in 1D) approximates this dispersion relation as simply a straight line, and from that calculates the heat capacity. But why bother doing that?? Wouldn't it be more accurate to use the proper dispersion relation to calculate the internal energy of the chain of atoms as a function of temperature? And this would just carry over to 3D, right? Why not just treat the atoms in the solid as a bunch of masses connected to each other with springs vibrating at various modes? Surely it isn't too difficult for a physicist with some grit to solve such a system? And how accurate is this mass-and-spring model anyways?