Update 8_many_atoms_solutions.md

src/8_many_atoms_solutions.md

@@ -144,7 +144,7 @@ Follow the same procedure as before but now using Ansatz $$ \begin{pmatrix} u_{1
 
 The eigenvalues are given by:
 
-$$ \omega^2 = \begin{pmatrix} \omega_1 \\ \omega_2 \\ \omega_3 \end{pmatrix} = \begin{pmatrix} q \\ k_3 + \frac{3q}{2} - \frac{\sqrt{4k_3^2 - 4k_3q + 9q^2}}{2} \\ k_3 + \frac{3q}{2} + \frac{\sqrt{4k_3^2 - 4k_3q + 9q^2}}{2} \end{pmatrix} $$
+$$ \omega^2 = \begin{pmatrix} \omega_1 \\ \omega_2 \\ \omega_3 \end{pmatrix} = \frac{1}{m} \begin{pmatrix} q \\ k_3 + \frac{3q}{2} - \frac{\sqrt{4k_3^2 - 4k_3q + 9q^2}}{2} \\ k_3 + \frac{3q}{2} + \frac{\sqrt{4k_3^2 - 4k_3q + 9q^2}}{2} \end{pmatrix} $$
 
 ### Subquestion 5