Solutions lecture 7

src/8_many_atoms_sol.md

@@ -11,10 +11,17 @@ configure_plotting()
 pi = np.pi
 ```
 
-# Solutions for lecture 7 exercises
+# Solutions for lecture 8 exercises
 
 ## Exercise 1: analyzing the diatomic vibrating chain
 
 ### Subquestion 1
 
+Accoustic branch corresponds with (-) in the equation given in the lecture notes. Use the small angle approximation $\sin(k) \approx k$ to ease calculations. For the taylor polynomial take $\omega^2 = f(x) = f(0) + f'(0)k + f''(0)k^2$ (some terms vanish). You should find: $$|v_g| = \sqrt{\frac{\kappa a^2}{2(m_a+m_2)}}$$
+
+### Subquestion 2
+
+Optical branch corresponds with (+) in the equation given in the lecture notes. Again use small angle approximation to easy calculations. Find the Taylor polynomial and show that $$|v_g|=0$$
+
+### Subquestion 3