Answer Happy

9. (12 points) In real metals, the effective forces are of quite long range. In other words, considering only the interaction between nearest neighbor atoms is too simple, i.e., it is just an ideal case. Show that the generalization of the dispersion relation to s nearest atoms in a one- dimensional monatomic chain is w2 = ()Σ %) { «s[1 – cos(ska)] – m s> where Ks is the spring constant corresponding to the force between s nearest atoms. Other variables are trivial or already defined in the above.