(c) At \( t=0 \), a particle is described by the wave function
\[
\Phi(x)=\frac{3}{5} \psi_{1}(x)-\frac{4}{5} \psi_{3}(x),
\]
where \( \psi_{1}(x) \) and \( \psi_{3}(x) \) are energy eigenstates with energies \( E_{1}=\hbar \omega_{1} \) and \( E_{3}=9 \hbar \omega_{1} \) respectively and \( \omega_{1} \) is a constant. Write down the corresponding time-dependent wave function \( \Phi(x, t) \). [2 marks]
Compute the frequency with which the associated probability distribution oscillates. [1 mark]