Question 2. A particle of mass m in the presence of an infinite potential well of width a starts out in the wave function \Psi(x, 0)=\left\{\begin{array}{ll}

\frac{2}{\sqrt{a}} \cos \frac{\pi x}{2 a} \sin \frac{3 \pi x}{2 a} & 0 \leq x \leq a \\

0 & \text { otherwise }

\end{array}\right. (a) Write the initial wave function as a superposition of stationary states (b) At time t > 0 the energy of the particle has been measured. What are the possible outcomes and what are the corresponding probabilities? Compute (H). (c) Compute (r) and (p) at time t = 0. State your answers as multiples of a.