diff --git a/src/8_many_atoms_sol.md b/src/8_many_atoms_sol.md index dfe0c65c46cf938d3c479fae85ab0170f03f1f2d..9648cb9dba106b5097f3b54b547d09a10950ce35 100644 --- a/src/8_many_atoms_sol.md +++ b/src/8_many_atoms_sol.md @@ -17,7 +17,7 @@ pi = np.pi ### 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 $\omega^2 = f(x) \approx f(0) + f'(0)k + f''(0)k^2$ (some terms vanish, computation is indeed quite tedious). You should find: $$|v_g| = \sqrt{\frac{\kappa a^2}{2(m_a+m_2)}}$$ +Accoustic branch corresponds with (-) in the equation given in the lecture notes. Use the small angle approximation $\sin(x) \approx x$ to ease calculations. For the Taylor polynomial take $\omega^2 = f(x) \approx f(0) + f'(0)k + f''(0)k^2$ (some terms vanish, computation is indeed quite tedious). You should find: $$|v_g| = \sqrt{\frac{\kappa a^2}{2(m_a+m_2)}}$$ ### Subquestion 2